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Mathematical and Theoretical Epidemiology and Ecology Models

Works Count: 56941

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Description

This cluster of papers focuses on mathematical modeling and analysis of disease transmission, population dynamics, and predator-prey interactions. It covers topics such as epidemic models, global stability, infectious diseases, Allee effects, and the use of stochastic differential equations to study these phenomena.

Keywords

Disease Transmission; Population Dynamics; Epidemic Models; Predator-Prey Interactions; Global Stability; Mathematical Modeling; Stochastic Differential Equations; Infectious Diseases; Allee Effects; Spatial Patterns

Mathematics in Population Biology

2003-12-31

Horst R. Thieme

The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected … The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results and ideas, organized by biological theme rather than mathematical concept, with an emphasis on helping the reader develop appropriate modeling skills through use of well-chosen and varied examples. Part I starts with unstructured single species population models, particularly in the framework of continuous time models, then adding the most rudimentary stage structure with variable stage duration. The theme of stage structure in an age-dependent context is developed in Part II, covering demographic concepts, such as life expectation and variance of life length, and their dynamic consequences. In Part III, the author considers the dynamic interplay of host and parasite populations, i.e., the epidemics and endemics of infectious diseases. The theme of stage structure continues here in the analysis of different stages of infection and of age-structure that is instrumental in optimizing vaccination strategies. Each section concludes with exercises, some with solutions, and suggestions for further study. The level of mathematics is relatively modest; a toolbox provides a summary of required results in differential equations, integration, and integral equations. In addition, a selection of Maple worksheets is provided. The book provides an authoritative tour through a dazzling ensemble of topics and is both an ideal introduction to the subject and reference for researchers.

Predation and Population Stability

1975-01-01

William W. Murdoch , Allan Oaten

Elements of mathematical ecology

2002-02-01

Mark Kot

Preface Part I. Unstructured Population Models Section A. Single Species Models: 1. Exponential, logistic and Gompertz growth 2. Harvest models - bifurcations and breakpoints 3. Stochastic birth and death processes … Preface Part I. Unstructured Population Models Section A. Single Species Models: 1. Exponential, logistic and Gompertz growth 2. Harvest models - bifurcations and breakpoints 3. Stochastic birth and death processes 4. Discrete-time models 5. Delay models 6. Branching processes Section B. Interacting Populations: 7. A classical predator-prey model 8. To cycle or not to cycle 9. Global bifurcations in predator-prey models 10. Chemosts models 11. Discrete-time predator-prey models 12. Competition models 13. Mutualism models Section C. Dynamics of Exploited Populations: 14. Harvest models and optimal control theory Part II. Structured Population Models Section D. Spatially-Structured Models: 15. Spatially-structured models 16. Spatial steady states: linear problems 17. Spatial steady states: nonlinear problems 18. Models of spread Section E. Age-Structured Models: 19. An overview of linear age-structured models 20. The Lokta integral equation 21. The difference equation 22. The Leslie matrix 23. The McKendrick-von Foerster PDE 24. Some simple nonlinear models Section F. Gender-Structured Models: 25. Two-sex models References Index.

Delay differential equations with applications in population dynamics

1993-11-01

Yang Kuang

Global Behavior of Nonlinear Difference Equations of Higher Order with Applications

1993-01-01

V. L. Kocic , G. Ladas

Monotone Dynamical Systems: An Introduction to the Theory of Competitive and Cooperative Systems

2008-03-26

Hal L. Smith

Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A … Monotone dynamical systems Stability and convergence Competitive and cooperative differential equations Irreducible cooperative systems Cooperative systems of delay differential equations Nonquasimonotone delay differential equations Quasimonotone systems of parabolic equations A competition model Appendix Bibliography.

Biodiversity of plankton by species oscillations and chaos

1999-11-01

Jef Huisman , Franz J. Weissing

Dispersion and Population Interactions

1974-03-01

Simon A. Levin

The spatial component of environment, often neglected in modeling of ecological interactions, in general operates to increase species diversity. This arises due to the heterogeneity of the environment, but such … The spatial component of environment, often neglected in modeling of ecological interactions, in general operates to increase species diversity. This arises due to the heterogeneity of the environment, but such heterogeneity can arise in an initially homogeneous environment due to what may be random initial events (e.g., colonization patterns), effects of which are magnified by species interactions. In this way, homogeneous environments may become heterogeneous and heterogeneous environments even more so. In patchy environments, distinct patches are likely to be colonized initially by different species, and thereby a kind of founder effect results whereby individual patches evolve along different paths simply as a consequence of initial colonization patterns. Species which would be unable to invade may nevertheless survive by establishing themselves early and will moreover be found in lower densities in other areas as overflow from their "safe" areas. Spatially continuous environments may evolve toward essentially patchy ones by this kind of process. Overall species richness is expected to be higher in patchy environments but to decrease as the ability of species to migrate becomes large. These results are due to patchiness per se and do not depend on the existence of several kinds of patches, a situation which will tend to reinforce these effects. Diversity is also increased in such environments with spatial extent due to the opportunities for fugitive-type spatio-temporal strategies. In these, local population oscillations provide the salvation for species which are for example competitively inferior or easy victims to predation but which can survive by superior migratory ability and (in patchy environments) talent for recolonization. Again, dependence is on spatial heterogeneity, in addition to temporal heterogeneity; again, this may be externally imposed or the result largely of internal processes. Some gross statistics for these processes, principally patch occupancy fractions, may prove useful for a simplified treatment of colonization-extinction equilibria, as in the approaches of Cohen (1970), Levins and Culver (1971), Horn and MacArthur (1972), and Slatkin (in preparation). For such considerations, however, one cannot assume independence of distributions; and the approach of Cohen (1970) and Slatkin (in preparation), which allows for consideration of covariance, is favored.

Some Characteristics of Simple Types of Predation and Parasitism

1959-07-01

C. S. Holling

In an earlier study (Holling, 1959) the basic and subsidiary components of predation were demonstrated in a predator-prey situation involving the predation of sawfly cocoons by small mammals. One of … In an earlier study (Holling, 1959) the basic and subsidiary components of predation were demonstrated in a predator-prey situation involving the predation of sawfly cocoons by small mammals. One of the basic components, termed the functional response, was a response of the consumption of prey by individual predators to changes of prey density, and it appeared to be at least theoretically important in population regulation: Because of this importance the functional response has been further examined in an attempt to explain its characteristics.

The Study of Population Growth in Organisms Grouped by Stages

1965-03-01

L. P. Lefkovitch

In this extension to the use of matrices in population mathematics (Lewis [1942] and Leslie [1945]), the division of a population into equal age groups is replaced by one of … In this extension to the use of matrices in population mathematics (Lewis [1942] and Leslie [1945]), the division of a population into equal age groups is replaced by one of unequal stage groups, no assumptions being made about the variation of the duration of the stage that different individuals may show. This extension has application in ecological studies where the age of an individual is rarely known. The model is briefly applied to three experimental situations.

A Model for Tropic Interaction

1975-07-01

Donald L. DeAngelis , Robert A. Goldstein , R. V. O’Neill

A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level … A nonlinear function general enough to include the effects of feeding saturation and intraspecific consumer interference is used to represent the transfer of material or energy from one trophic level to another. The function agrees with some recent experimental data on feeding rates. A model using this feeding rate function is subjected to equilibrium and stability analyses to ascertain its mathematical implications. The anaylses lead to several observations; for example, increases in maximum feeding rate may, under certain circumstances; result in decreases in consumer population and mutal interference between consumers is a major stabilizing factor in a nonlinear system. The analyses also suggest that realistic classes of consumer—resource models exist which do not obey Kolmogorov's Criteria but are nevertheless globally stable.

Optimal foraging, the marginal value theorem

1976-04-01

Eric L. Charnov

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A generalization of the Kermack-McKendrick deterministic epidemic model

1978-11-01

Vincenzo Capasso , Gabriella Serio

Introduction to the Mathematics of Population.

1970-09-01

Samuel Goldberg , Nathan Keyfitz

Environmental Variability Promotes Coexistence in Lottery Competitive Systems

1981-06-01

Peter Chesson , Robert R. Warner

In deterministic approaches to modeling, two species are generally regarded as capable of coexistence if the model has a stable equilibrium with both species in positive numbers. Temporal environmental variability … In deterministic approaches to modeling, two species are generally regarded as capable of coexistence if the model has a stable equilibrium with both species in positive numbers. Temporal environmental variability is assumed to reduce the likelihood of coexistence by keeping species abundances away from equilibrium. Here we present a contrasting view based on a model of competition for space among coral reef fishes, or any similarly territorial animals. The model has no stable equilibrium point with both species in positive abundance, yet both species persist in the system provided environmental variability in birth rates is sufficiently high. In general the higher the environmental variability the more likely it is that coexistence will occur. This conclusion is not affected by one species having a mean advantage over the other. Not all kinds of environmental variability necessarily lead to coexistence, however, for when the death rates of the two species are highly variable and negatively correlated, the extinction of one species, determined by chance, is likely to occur. The results in this paper are shown to depend on the nonlinearity of the dynamics of the system. This nonlinearity arises from the simple fact that the animals have overlapping generations. When applied to the coral reef fish setting, our analysis confirms the view that coexistence can occur in a system where space is allocated largely at random, provided environmental variability is sufficiently great (Sale 1977); but our explanations and predictions differ in detail with those of Sale.

Dispersal Data and the Spread of Invading Organisms

1996-10-01

Mark Kot , Mark A. Lewis , P. van den Driessche

Models that describe the spread of invading organisms often assume that the dispersal distances of propagules are normally distributed. In contrast, measured dispersal curves are typically leptokurtic, not normal. In … Models that describe the spread of invading organisms often assume that the dispersal distances of propagules are normally distributed. In contrast, measured dispersal curves are typically leptokurtic, not normal. In this paper, we consider a class of models, integrodifference equations, that directly incorporate detailed dispersal data as well as population growth dynamics. We provide explicit formulas for the speed of invasion for compensatory growth and for different choices of the propagule redistribution kernel and apply these formulas to the spread of D. pseudoobscura. We observe that: (1) the speed of invasion of a spreading population is extremely sensitive to the precise shape of the redistribution kernel and, in particular, to the tail of the distribution; (2) fat—tailed kernels can generate accelerating invasions rather than constant—speed travelling waves; (3) normal redistribution kernels (and by inference, many reaction—diffusion models) may grossly underestimate rates of spread of invading populations in comparison with models that incorporate more realistic leptokurtic distributions; and (4) the relative superiority of different redistribution kernels depends, in general, on the precise magnitude of the net reproductive rate. The addition of an Allee effect to an integrodifference equation may decrease the overall rate of spread. An Allee effect may also introduce a critical range; the population must surpass this spatial threshold in order to invade successfully. Fat—tailed kernels and Allee effects provide alternative explanations for the accelerating rates of spread observed for many invasions.

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Coupling in predator-prey dynamics: Ratio-Dependence

1989-08-01

Roger Arditi , Lev R. Ginzburg

The Ecology of Fear: Optimal Foraging, Game Theory, and Trophic Interactions

1999-05-20

J. S. Brown , J. W. Laundre , M. B. Gurung

Mammalian predator-prey systems are behaviorally sophisticated games of stealth and fear. But, traditional mass-action models of predator prey dynamics treat individuals as behaviorally unresponsive “molecules” in Brownian motion. Foraging theory … Mammalian predator-prey systems are behaviorally sophisticated games of stealth and fear. But, traditional mass-action models of predator prey dynamics treat individuals as behaviorally unresponsive “molecules” in Brownian motion. Foraging theory should provide the conceptual framework to envision the interaction. But, current models of predator feeding behavior generally envision a clever predator consuming large numbers of sessile and behaviorally inert prey (e.g., kangaroo rats, Dipodomys, collecting seeds from food patches). Here, we extend foraging theory to consider a predator-prey game of stealth and fear and then embed this game into the modeling of predator-prey population dynamics. The melding of the prey and predator's optimal behaviors with their population and community-level consequences constitutes the ecology of fear. The ecology of fear identifies the endpoints of a continuum of N-driven (population size) versus μ-driven (fear) systems. In N-driven systems, the major direct dynamical feedback involves predators killing prey, whereas μ-driven systems involve the indirect effects from changes in fear levels and prey catchability. In μ-driven systems, prey respond to predators by becoming more vigilant or by moving away from suspected predators. In this way, a predator (e.g., mountain lion, Puma concolor) depletes a food patch (e.g., local herd of mule deer, Odocoileus hemionus) by frightening prey rather than by actually killing prey. Behavior buffers the system: a reduction in predator numbers should rapidly engender less vigilant and more catchable prey. The ecology of fear explains why big fierce carnivores should be and can be rare. In carnivore systems, ignore the behavioral game at one's peril.

Bifurcations and Dynamic Complexity in Simple Ecological Models

1976-07-01

Robert M. May , George Oster

Many biological populations breed seasonally and have nonoverlapping generations, so that their dynamics are described by first-order difference equations, Nt+1 = F (Nt). In many cases, F(N) as a function … Many biological populations breed seasonally and have nonoverlapping generations, so that their dynamics are described by first-order difference equations, Nt+1 = F (Nt). In many cases, F(N) as a function of N will have a hump. We show, very generally, that as such a hump steepens, the dynamics goes from a stable point, to a bifurcating hierarchy of stable cycles of period 2n, into a region of chaotic behavior where the population exhibits an apparently random sequence of "outbreaks" followed by "crashes." We give a detailed account of the underlying mathematics of this process and review other situations (in two- and higher dimensional systems, or in differential equation systems) where apparently random dynamics can arise from bifurcation processes. This complicated behavior, in simple deterministic models, can have disturbing implications for the analysis and interpretation of biological data.

Multidimensional nonlinear diffusion arising in population genetics

1978-10-01

D. G. Aronson , Hans F. Weinberger

The approach of solutions of nonlinear diffusion equations to travelling front solutions

1977-12-01

Paul C. Fife , J. B. McLeod

Predation, apparent competition, and the structure of prey communities

1977-10-01

Robert D. Holt

Switching in General Predators: Experiments on Predator Specificity and Stability of Prey Populations

1969-09-01

William W. Murdoch

"Switching" in predators which attack several prey species potentially can stabilize the numbers in prey populations. In switching, the number of attacks upon a species is disproportionately large when the … "Switching" in predators which attack several prey species potentially can stabilize the numbers in prey populations. In switching, the number of attacks upon a species is disproportionately large when the species is abundant relative to other prey, and disproportionately small when the species is relatively rare. The null case for two prey species can be written: P 1 /P 2 = cN 1 /N 2 , where P 1 /P 2 is the ratio of the two prey expected in the diet, N 1 /N 2 is the ratio given and c is a proportionality constant. Predators were sea—shore snails and prey were mussels and barnacles. Experiments in the laboratory modelled aspects of various natural situations. When the predator had a strong preference (c) between prey the data and the "null case" model were in good agreement. Preference could not altered by subjecting predators to training regimens. When preference was weak the data did not fit the model replicates were variable. Predators could be trained easily to one or other prey species. From a number of experiments it was concluded that in the weak—preference case no switch would occur in nature except where there is an opportunity for predators to become trained to the abundant species. A patchy distribution of the abundant prey could provide this opportunity. Given one prey species, snails caused a decreasing percentage mortality as prey numbers increased. This occurred also with 2 prey species present when preference was strong. When preference was weak the form of the response was unclear. When switching occurred the percentage prey mortality increased with prey density, giving potentially stabilizing mortality. The consequences of these conclusions for prey population regulation and for diversity are discussed.

On the dynamics of exploited fish populations

1994-06-01

Raymond J. H. Beverton , Sidney J. Holt

On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations

1990-06-01

Odo Diekmann , Hans Heesterbeek , J.A.J. Metz

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Nonlinear Aspects of Competition Between Three Species

1975-09-01

Robert M. May , Warren J. Leonard

It is shown that for three competitors, the classic Gause–Lotka–Volterra equations possess a special class of periodic limit cycle solutions, and a general class of solutions in which the system … It is shown that for three competitors, the classic Gause–Lotka–Volterra equations possess a special class of periodic limit cycle solutions, and a general class of solutions in which the system exhibits nonperiodic population oscillations of bounded amplitude but ever increasing cycle time. Biologically, the result is interesting as a caricature of the complexities that nonlinearities can introduce even into the simplest equations of population biology ; mathematically, the model illustrates some novel tactical tricks and dynamical peculiarities for 3-dimensional nonlinear systems.

Graphical Representation and Stability Conditions of Predator-Prey Interactions

1963-07-01

Michael L. Rosenzweig , Robert H. MacArthur

The general nature of the predator-prey interaction has been depicted as a graph of predator versus prey densities from which conditions for stability of the interaction are predicted. An example … The general nature of the predator-prey interaction has been depicted as a graph of predator versus prey densities from which conditions for stability of the interaction are predicted. An example of a three-species interaction is also presented. Variations of the graph are introduced, and it is shown that an otherwise unstable interaction may be stabilized by the presence of either an inviolable prey hiding place, or extremely low predation pressure at moderate predator and high prey densities, or another predator-limiting resource. Stability is always conferred when the predator is severely limited at its equilibrium density by one of its resources other than its supply of prey. Predators should tend to be limited at their equilibrium densities by more than one of their resources. When either of the two foregoing situations pertains, regular predator-prey oscillations should not be observable. The stability of the interaction close to equilibrium was found to depend exclusively, in the mathematically-continuous model, upon the slopes of two lines in the graph at equilibrium. Stability can be asymptotic rather than oscillatory in type. An equation for the period of oscillatory interactions is also advanced. The effects of Natural Selection on the isoclines, and thus the stability, is not clear-cut. Selection of the prey tends to stabilize the interaction; the opposite is true for selection on the predator.

Biological Populations with Nonoverlapping Generations: Stable Points, Stable Cycles, and Chaos

1974-11-15

Robert M. May

Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable … Some of the simplest nonlinear difference equations describing the growth of biological populations with nonoverlapping generations can exhibit a remarkable spectrum of dynamical behavior, from stable equilibrium points, to stable cyclic oscillations between 2 population points, to stable cycles with 4, 8, 16, . . . points, through to a chaotic regime in which (depending on the initial population value) cycles of any period, or even totally aperiodic but boundedpopulation fluctuations, can occur. This rich dynamical structure is overlooked in conventional linearized analyses; its existence in such fully deterministic nonlinear difference equations is a fact of considerable mathematical and ecological interest.

A General Hypothesis of Species Diversity

1979-01-01

Michael A. Huston

A new hypothesis, based on differences in the rates at which populations of competing species approach competitive equilibrium (reduction or exclusion of some species), is proposed to explain patterns of … A new hypothesis, based on differences in the rates at which populations of competing species approach competitive equilibrium (reduction or exclusion of some species), is proposed to explain patterns of species diversity. The hypothesis assumes that most communities exist in a state of nonequilibrium where competitive equilibrium is prevented by periodic population reductions and environmental fluctuations. When competitive equilibrium is prevented, a dynamic balance may be established between the rate of competitive displacement and the frequency of population reduction, which results in a stable level of diversity. Under conditions of infrequent reductions, an increase in the population growth rates of competitors generally results in decreased diversity. This model clarifies an underlying pattern of variation in diversity and points out the common elements of previous hypotheses. Rather than arguing that either competition, predation, or productivity control diversity, it demonstrates that all of these may contribute to the same basic mechanism. In doing so, it not only explains the correlations of the other hypotheses with patterns of diversity, but also explains the exceptions that these hypotheses could not explain. This hypothesis may be applied to variations of diversity both on a latitudinal gradient and within specific regions.

Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time

1971-01-29

Michael L. Rosenzweig

Six reasonable models of trophic exploitation in a two-species ecosystem whose exploiters compete only by depleting each other's resource supply are presented. In each case, increasing the supply of limiting … Six reasonable models of trophic exploitation in a two-species ecosystem whose exploiters compete only by depleting each other's resource supply are presented. In each case, increasing the supply of limiting nutrients or energy tends to destroy the steady state. Thus man must be very careful in attempting to enrich an ecosystem in order to increase its food yield. There is a real chance that such activity may result in decimation of the food species that are wanted in greater abundance.

Variations and Fluctuations of the Number of Individuals in Animal Species living together

1928-04-01

Vito Volterra

Variations and Fluctuations of the Number of Individuals in Animal Species living together Get access Vito Volterra Vito Volterra Professor Translated by Miss Mary Evelyn Wells, Doctor of MathematicsRome Search … Variations and Fluctuations of the Number of Individuals in Animal Species living together Get access Vito Volterra Vito Volterra Professor Translated by Miss Mary Evelyn Wells, Doctor of MathematicsRome Search for other works by this author on: Oxford Academic Google Scholar ICES Journal of Marine Science, Volume 3, Issue 1, April 1928, Pages 3–51, https://doi.org/10.1093/icesjms/3.1.3 Published: 01 April 1928

Risks of Population Extinction from Demographic and Environmental Stochasticity and Random Catastrophes

1993-12-01

Russell Lande

Stochastic factors affecting the demography of a single population are analyzed to determine the relative risks of extinction from demographic stochasticity, environmental stochasticity, and random catastrophes. Relative risks are assessed … Stochastic factors affecting the demography of a single population are analyzed to determine the relative risks of extinction from demographic stochasticity, environmental stochasticity, and random catastrophes. Relative risks are assessed by comparing asymptotic scaling relationships describing how the average time to extinction, T, increases with the carrying capacity of a population, K, under each stochastic factor alone. Stochastic factors are added to a simple model of exponential growth up to K. A critical parameter affecting the extinction dynamics is $$\tilde r,$$ the long-run growth rate of a population below K, including stochastic factors. If r̃ is positive, with demographic stochasticity T increases asymptotically as a nearly exponential function of K, and with either environmental stochasticity or random catastrophes T increases asymptotically as a power of K. If r̃ is negative, under any stochastic demographic factor, T increases asymptotically with the logarithm of K. Thus, for sufficiently large populations, the risk of extinction from demographic stochasticity is less important than that from either environmental stochasticity or random catastrophes. The relative risks of extinction from environmental stochasticity and random catastrophes depend on the mean and environmental variance of population growth rate, and the magnitude and frequency of catastrophes. Contrary to previous assertions in the literature, a population of modest size subject to environmental stochasticity or random catastrophes can persist for a long time, if r̃ is substantially positive.

Stability and Oscillations in Delay Differential Equations of Population Dynamics

1992-01-01

K. Gopalsamy

Dynamical Models of Tuberculosis and Their Applications

2004-01-01

Carlos Castillo‐Chávez , Baojun Song

The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed … The reemergence of tuberculosis (TB) from the 1980s to the early 1990s instigated extensive researches on the mechanisms behind the transmission dynamics of TB epidemics. This article provides a detailed review of the work on the dynamics and control of TB. The earliest mathematical models describing the TB dynamics appeared in the 1960s and focused on the prediction and control strategies using simulation approaches. Most recently developed models not only pay attention to simulations but also take care of dynamical analysis using modern knowledge of dynamical systems. Questions addressed by these models mainly concentrate on TB control strategies, optimal vaccination policies, approaches toward the elimination of TB in the U.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responses of the immune system, impacts of demography, the role of public transportation systems, and the impact of contact patterns. Model formulations involve a variety of mathematical areas, such as ODEs (Ordinary Differential Equations) (both autonomous and non-autonomous systems), PDEs (Partial Differential Equations), system of difference equations, system of integro-differential equations, Markov chain model, and simulation models.

Optimal Foraging: A Selective Review of Theory and Tests

1977-06-01

Graham H. Pyke , H. Ronald Pulliam , Eric L. Charnov

Beginning with Emlen (1966) and MacArthur and Pianka (1966) and extending through the last ten years, several authors have sought to predict the foraging behavior of animals by means of … Beginning with Emlen (1966) and MacArthur and Pianka (1966) and extending through the last ten years, several authors have sought to predict the foraging behavior of animals by means of mathematical models. These models are very similar,in that they all assume that the fitness of a foraging animal is a function of the efficiency of foraging measured in terms of some "currency" (Schoener, 1971) -usually energy- and that natural selection has resulted in animals that forage so as to maximize this fitness. As a result of these similarities, the models have become known as "optimal foraging models"; and the theory that embodies them, "optimal foraging theory." The situations to which optimal foraging theory has been applied, with the exception of a few recent studies, can be divided into the following four categories: (1) choice by an animal of which food types to eat (i.e., optimal diet); (2) choice of which patch type to feed in (i.e., optimal patch choice); (3) optimal allocation of time to different patches; and (4) optimal patterns and speed of movements. In this review we discuss each of these categories separately, dealing with both the theoretical developments and the data that permit tests of the predictions. The review is selective in the sense that we emphasize studies that either develop testable predictions or that attempt to test predictions in a precise quantitative manner. We also discuss what we see to be some of the future developments in the area of optimal foraging theory and how this theory can be related to other areas of biology. Our general conclusion is that the simple models so far formulated are supported are supported reasonably well by available data and that we are optimistic about the value both now and in the future of optimal foraging theory. We argue, however, that these simple models will requre much modification, espicially to deal with situations that either cannot easily be put into one or another of the above four categories or entail currencies more complicated that just energy.

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A Practical Model of Metapopulation Dynamics

1994-01-01

Ilkka Hanski

This paper describes a novel approach to modelling of metapopulation dynamics. The model is constructed as a generalized incidence function, which describes how the fraction of occupied habitat patches depends … This paper describes a novel approach to modelling of metapopulation dynamics. The model is constructed as a generalized incidence function, which describes how the fraction of occupied habitat patches depends on patch areas and isolations. The model may be fitted to presence/absence data from a metapopulation at a dynamic equilibrium between extinctions and colonizations. Using the estimated parameter values, transient dynamics and the equilibrium fraction of occupied patches in any system of habitat patches can be predicted. The significance of particular habitat patches for the long-term persistence of the metapopulation, for example, can also be evaluated

Determining Important Parameters in the Spread of Malaria Through the Sensitivity Analysis of a Mathematical Model

2008-02-21

Nakul Chitnis , James M. Hyman , J. M. Cushing

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Simple mathematical models with very complicated dynamics

1976-06-10

Robert M. May

Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission

2002-11-01

P. van den Driessche , James Watmough

The Mathematics of Infectious Diseases

2000-01-01

Herbert W. Hethcote

Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number … Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number $R_{0}$, the contact number $\sigma$, and the replacement number R are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of $R_{0}$ and $\sigma$ are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.

On the Dynamics of Exploited Fish Populations.

1959-12-01

F. N. David , R. J. H. Beverton , Sidney J. Holt

On the Dynamics of Exploited Fish Populations

1958-08-28

Raymond J. H. Beverton , Sidney J. Holt

Lotka–Volterra-type kinetic equations for interacting species

2025-06-25

Andrea Bondesan , Marco Menale , Giuseppe Toscani +1 more | Nonlinearity

Abstract In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator–prey interactions. The model builds upon the … Abstract In this work, we examine a kinetic framework for modeling the time evolution of size distribution densities of two populations governed by predator–prey interactions. The model builds upon the classical Boltzmann-type equations, where the dynamics arise from elementary binary interactions between the populations. The model uniquely incorporates a linear redistribution operator to quantify the birth rates in both populations, inspired by wealth redistribution operators. We prove that, under a suitable scaling regime, the Boltzmann formulation transitions to a system of coupled Fokker–Planck-type equations. These equations describe the evolution of the distribution densities and link the macroscopic dynamics of their mean values to a Lotka–Volterra system of ordinary differential equations, with parameters explicitly derived from the microscopic interaction rules. We then determine the local equilibrium of the Fokker–Planck system, which are Gamma-type densities, and investigate the problem of relaxation of its solutions toward these kinetic equilibrium, in terms of their moments’ dynamics. The results establish a bridge between kinetic modeling and classical population dynamics, offering a multiscale perspective on predator–prey systems.

Qualitative Behavior of a Discrete‐Time Predator–Prey Model With Holling‐Type III Functional Response and Gompertz Growth of Prey

2025-06-25

M‎. ‎B‎. Almatrafi , Messaoud Berkal , M. Y. Hamada | Mathematical Methods in the Applied Sciences

ABSTRACT This paper investigates the bifurcation dynamics of a discrete‐time predator–prey model with a Holling‐type III functional response and Gompertz growth for the prey. Using the forward Euler discretization, we … ABSTRACT This paper investigates the bifurcation dynamics of a discrete‐time predator–prey model with a Holling‐type III functional response and Gompertz growth for the prey. Using the forward Euler discretization, we analyze the local stability of fixed points and explore the occurrence of flip and Neimark–Sacker bifurcations. Additionally, we employ state feedback control to regulate chaotic behavior. Numerical simulations illustrate the impact of parameter variations on system dynamics, complementing the theoretical analysis. This study provides insights into the complex behaviors that arise in discrete predator–prey interactions.

Impact of prey herd behavior and predator hunting cooperation on eco-epidemic dynamics with impulsive harvesting control: a real-data approach

2025-06-25

Paul P. Tessy , Mst Sebi Khatun , Pritha Das | The European Physical Journal Plus

On Bifurcation of a Single‐Species Model With Stage Structure and Harvest

2025-06-24

Honghua Bin , Yuying Liu , Junjie Wei | Mathematical Methods in the Applied Sciences

ABSTRACT In this paper, the Nicholson's blowflies equation with stage structure and harvest is investigated. By employing the property of Lambert function, the existence of positive equilibria is obtained. With … ABSTRACT In this paper, the Nicholson's blowflies equation with stage structure and harvest is investigated. By employing the property of Lambert function, the existence of positive equilibria is obtained. With aid of the distribution of the eigenvalues in the characteristic equation, the local stability of the equilibria and the existence of Hopf bifurcation of the single‐species model are obtained. Furthermore, it is found that when the harvest rate is sufficiently small, the directions of the Hopf bifurcations at the first and last bifurcation values are forward and backward, respectively, and the bifurcating periodic solutions are all asymptotically stable. Numerical simulations are carried out to illustrate the theoretical analysis.

Stationary distribution of a stochastic SEIR model with infectivity in the incubation period and homestead-isolation on the susceptible under regime switching

2025-06-24

Ying He , Bo Bi | Journal of Biological Dynamics

This paper is concerned with a stochastic SEIR model with infectivity in the incubation period and homestead-isolation on the susceptible, which is perturbed by white and colour noises. The model … This paper is concerned with a stochastic SEIR model with infectivity in the incubation period and homestead-isolation on the susceptible, which is perturbed by white and colour noises. The model has a unique stationary distribution, which reflects the persistence of epidemics over a long period. Using the Has-minskii theorem and constructing stochastic Lyapunov functions with regime switching, we derive an important condition R0s. Comparing the expression for R0 and R0s, we can see that if there is no environmental noise, then R0s=R0. It ensures the asymptotic stability of the positive equilibrium E∗ of the corresponding deterministic system.

Mathematical Analysis of a Predator–Prey Model Incorporating Prey Fear

2025-06-24

Mónica Patricia Martínez Ordoñez , Jhelly Pérez , Neisser Pino Romero | Proyecciones (Antofagasta)

Este estudio analiza un ecosistema depredador-presa en el que la presa sirve como fuente de alimento preferida del depredador. El crecimiento de la población de presas está limitado por dos … Este estudio analiza un ecosistema depredador-presa en el que la presa sirve como fuente de alimento preferida del depredador. El crecimiento de la población de presas está limitado por dos factores principales: la disponibilidad de recursos ambientales y el miedo inducido por la presencia del depredador. Por otro lado, el crecimiento de la población de depredadores está restringido por la disponibilidad tanto de presas como de una fuente de alimento alternativa. Se asume que el tiempo que los depredadores dedican a perseguir, someter, consumir y digerir a sus presas, junto con el tiempo necesario para prepararse para la siguiente cacería, depende del número de individuos en ambas poblaciones. El trabajo consiste en un análisis cualitativo exhaustivo de las soluciones al sistema de ecuaciones asociado con el modelo propuesto. Estos resultados analíticos se validan posteriormente mediante simulaciones numéricas implementadas en Python. Además, se realiza un estudio comparativo con un modelo similar que no incorpora la respuesta de miedo de la presa al depredador.

Dynamic analysis of a fractional order three-dimensional predator-prey system with competitive and fear effects

2025-06-24

Binfeng Xie , Zhengce Zhang , Na Zhang | Nonlinear Dynamics

Modeling and Dynamic Analysis for a Three-Species Model: With and Without Time Delay

2025-06-24

Xin Zhang | Results in Mathematics

A Mathematical Model for Allergic Reactions Induced by the Therapy of HIV

2025-06-24

Rawan Abdullah , Florin Avram , A. Halanay +1 more | Mathematical Methods in the Applied Sciences

ABSTRACT A new mathematical model for cell evolution in HIV is introduced and studied. Delay differential equations are used to capture the dynamics of immune system cells involved in allergies, … ABSTRACT A new mathematical model for cell evolution in HIV is introduced and studied. Delay differential equations are used to capture the dynamics of immune system cells involved in allergies, as well as the evolution of HIV viruses, infected and uninfected CD4 cells, and cytotoxic T‐lymphocytes, under specific antiretroviral therapy. The model extends prior work by incorporating time delays to reflect the latency in immune response and drug effects, as well as interactions between the immune system and viral dynamics. Essential qualitative properties of the solutions, such as nonnegativity and global existence, are proved, ensuring the biological feasibility of the model. A partial stability analysis is conducted for some steady states of the system using Lyapunov‐Krasovskii functionals. Biological interpretation of partial stability results are given and the interplay between infected cells and immune responses during HIV treatment is further explored, with a particular focus on mitigating allergic reactions induced by medication. Numerical simulations are employed to illustrate the impact of these interactions and evaluate the effectiveness of treatment strategies.

Traveling Waves in a Reaction-Diffusion Addiction Epidemic Model with Distributed Delays

2025-06-23

Hamid Toumi , Khaled Boudjema Djeffal , Abdelheq Mezouaghi +2 more | Acta Applicandae Mathematicae

Evolution of harvesting in competitive population dynamics with spatial heterogeneity

2025-06-23

M.T. Valero Adán | GANIT Journal of Bangladesh Mathematical Society

The study investigates the intricate interactions, particularly the antagonistic dynamics, between two entities inhabiting a nonhomogeneous circumstance subjected to harvesting pressures. We initiate our analysis by constructing a robust mathematical … The study investigates the intricate interactions, particularly the antagonistic dynamics, between two entities inhabiting a nonhomogeneous circumstance subjected to harvesting pressures. We initiate our analysis by constructing a robust mathematical framework utilizing partial differential equations (PDEs) to model the behaviors of the two species. We rigorously demonstrate the substantiality and exclusivity of solutions to the formulated model. In this context, we establish pivotal conditions that facilitate species coexistence, as well as delineate scenarios wherein one species may exert competitive pressures sufficient to drive the other towards extinction. Additionally, we identify conditions that could culminate in the simultaneous extinction of both species. The findings yield a comprehensive relative analysis of two distinct harvesting levels, providing critical insights into their differential impacts on species dynamics. Furthermore, we substantiate our theoretical conclusions through a series of numerical simulations, which serve to validate our model and its implications. J. Bangladesh Math. Soc. 45.1 (2025) 32–49

Dynamics of a Tri-Trophic Predation Model with Antipredator Behavior and Beddington-DeAngelis Functional Response

2025-06-23

Xiangxiang Jin , Jie Li , Lingling Liu | Qualitative Theory of Dynamical Systems

Optimal Control of an Eco-Epidemiological Reaction-Diffusion Model

2025-06-22

Runmei Du , X.-Y. Liang , Na Yang +1 more | Mathematics

In this paper, a prey–predator diffusion model with isolation and drug treatment control measures for prey infection is studied. The main objective is to find an optimal control that minimizes … In this paper, a prey–predator diffusion model with isolation and drug treatment control measures for prey infection is studied. The main objective is to find an optimal control that minimizes the population density of infected prey and the costs of isolation and drug treatment for infected prey. Through analysis, the existence and uniqueness of weak solution, as well as the existence and local uniqueness of optimal controls are proven. The first-order necessary condition is derived, and the feasibility of the theoretical proof is verified through numerical simulations.

A Comparative Analysis of Harmonic Mean, Holling Type II, Beddington–DeAngelis, and Crowley–Martin Incidence Rates of a Piecewise Dengue Fever Dynamics Model

2025-06-22

Faten H. Damag , Ashraf Ahmed Qurtam , Mohammed A. ‬Almalahi +4 more | Fractal and Fractional

Dengue fever remains a major global health threat, and mathematical models are crucial for predicting its spread and evaluating control strategies. This study introduces a highly flexible dengue transmission model … Dengue fever remains a major global health threat, and mathematical models are crucial for predicting its spread and evaluating control strategies. This study introduces a highly flexible dengue transmission model using a novel piecewise fractional derivative framework, which can capture abrupt changes in epidemic dynamics, such as those caused by public health interventions or seasonal shifts. We conduct a rigorous comparative analysis of four widely used but distinct mechanisms of disease transmission (incidence rates): Harmonic Mean, Holling Type II, Beddington–DeAngelis, and Crowley–Martin. The model’s well-posedness is established, and the basic reproduction number (ℜ0) is derived for each incidence function. Our central finding is that the choice of this mathematical mechanism critically alters predictions. For example, models that account for behavioral changes (Beddington–DeAngelis, Crowley–Martin) identify different key drivers of transmission compared to simpler models. Sensitivity analysis reveals that vector mortality is the most influential control parameter in these more realistic models. These results underscore that accurately representing transmission behavior is essential for reliable epidemic forecasting and for designing effective, targeted intervention strategies.

Investigation of spatial pattern in mussel-algae model with higher-order interactions and PD control

2025-06-20

Shuang Dai , Min Xiao , Chengdai Huang +2 more | The European Physical Journal Plus

Predation model with prey-dependent carrying capacity for predators

2025-06-20

Fengqin Zhang , Xinxin Ren , Hanwu Liu | International Journal of Biomathematics

Stability of an HIV-1 abortive infection model with antibody immunity and delayed inflammatory cytokine production

2025-06-20

A. M. Ełaiw , Elsayed Dahy , H. Z. Zidan +1 more | The European Physical Journal Plus

Disease Dynamics of Stochastic SEIQHR Model with Dispersal

2025-06-20

Kazi Hafizur Rahman , Chandra Nath Podder | Journal of Biological Systems

Influence of Additional Food and Brownian Movement on the Dynamics of Pest-Predator Model

2025-06-20

Shivam Shivam , Teekam Singh , Anupam Singh | Journal of Biological Systems

Generalized virus spreading dynamics inspired by mixing risky strategies

2025-06-20

H. R. Qi , Yue Yao , Wei Zhao +5 more | International Journal of Modern Physics C

A fractional-order Bertrand duopoly model with bounded rationality and heterogeneous expectations and its application in high-security image encryption

2025-06-20

Haneche Nabil , Tayeb Hamaizia | Physica Scripta

Abstract Mathematical modeling is crucial for understanding dynamical systems and nonlinear phenomena. However, several mathematical models developed for systems incorporate either integer-order derivatives or continuous fractional-order derivatives. Due to the … Abstract Mathematical modeling is crucial for understanding dynamical systems and nonlinear phenomena. However, several mathematical models developed for systems incorporate either integer-order derivatives or continuous fractional-order derivatives. Due to the memory effect and hereditary properties, fractional-order equations and systems have been extensively used for modeling several real-world phenomena in biology, finance, physics, and engineering. This study presents a novel fractional-order Bertrand-type duopoly model that involves maximization of relative profits and a cost function including externalities. The fractional model is constructed using the Caputo-like delta operator. The competition is described by nonlinear difference equations, with variables representing the pricing of products distributed by firms. The nonlinear dynamic properties of the competition's map, which include chaotic dynamic behaviors, complexity analysis, and synchronization, are investigated. The stability of the Nash equilibrium of the fractional-order model is analyzed based on the stability theory of discrete-time fractional-order maps. Furthermore, using a nonlinear fractional controller, a chaotic synchronization between two identical Bertrand duopoly systems is achieved. Additionally, the proposed chaotic synchronization scheme serves as a practical application for grayscale image encryption. Several experimental tests are provided to verify the security and performance of the proposed image cryptosystem.

Dynamic complexity of a delayed spatiotemporal predator-prey model

2025-06-19

Mohamed Hafdane , Nossaiba Baba , Youssef El Foutayeni +1 more | Frontiers in Applied Mathematics and Statistics

This study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed … This study investigates a delayed spatiotemporal predator-prey model that incorporates key ecological mechanisms, including the Allee effect, fear-induced prey behavior, Holling type II predation with cooperative hunting, toxicity with delayed effects, and both nonlinear (for prey) and linear (for predators) fishing pressures. Using tools from the theory of partial differential equations, stability analysis, and Hopf bifurcation theory, we derive the conditions under which stable coexistence or instability emerges. Our results reveal that system stability is maintained below a critical delay threshold, beyond which oscillatory dynamics arise. In the spatial domain, diffusion can either stabilize populations or lead to heterogeneous patterns such as Turing structures and predator-prey segregation, particularly when diffusion is low and delays are significant. Numerical simulations support and illustrate the analytical findings, showing a variety of dynamic behaviors consistent with observed ecological patterns. This work highlights how the interplay between ecological processes, time delays, and spatial effects governs predator-prey dynamics and offers insights relevant to ecosystem management.

Dynamics stability of a delayed eco-epidemic predator-prey system: the interplay of cooperative hunting and fear effects

2025-06-19

Benamara Ibtissam , Ibrihich Ouafaa , Lasri Imane +1 more | International Journal of Dynamics and Control

Qualitative analysis of fractal–fractional order Coffee Berry epidemic model on an agricultural farm

2025-06-18

M. Suresh Kumar , N. Ramesh Babu , S. Harshavarthini +1 more | Results in Physics

A Structured Predator–Prey Model with a State-Dependent Maturation Period

2025-06-18

Wenxian Sun , Ning Wang , Nannan Li +2 more | International Journal of Bifurcation and Chaos

In this paper, we introduce a novel predator–prey model that accounts for the impact of the juvenile predator population size during its mature period. The model incorporates a nonlinear feedback … In this paper, we introduce a novel predator–prey model that accounts for the impact of the juvenile predator population size during its mature period. The model incorporates a nonlinear feedback growth rate, and we analyze its dynamics by transforming it into three forms using the characteristic method and time scales. We establish global threshold dynamics of the system based on the net reproductive number of predators, as well as criteria for the local asymptotic stability of the coexistence equilibrium. To validate these theoretical findings, numerical simulations are then implemented, enabling direct comparison between the model’s behavior and that of its constant-delay equivalent. Our results provide valuable insights into the effects of state-dependent maturation delay on predator–prey dynamics, and we offer a framework for comprehending and predicting population predation in structured populations.

Fear of Predation and its Carry-Over Effect in a Fractional Order Prey-Predator Model with Double Allee Effect

2025-06-18

Hatice Çizmeci , Ercan Balcı | International Journal of Applied and Computational Mathematics

Interface Dynamics in Nonlocal Dispersal Fisher-KPP Equations

2025-06-18

Tao Wen , Wan‐Tong Li , Jian‐Wen Sun +1 more | Acta Mathematica Scientia

Asymptotic Stability of a Rumor Spreading Model with Three Time Delays and Two Saturation Functions

2025-06-18

Teng Sheng , Chunlong Fu , Xiaofan Yang +2 more | Mathematics

Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. … Time delays and saturation effects are critical elements describing complex rumor spreading behaviors. In this article, a rumor spreading model with three time delays and two saturation functions is proposed. The basic properties of the model are reported. The structure of the rumor-endemic equilibria is deduced. A criterion for the global asymptotic stability of the rumor-free equilibrium is derived. In the presence of very small delays, a criterion for the local asymptotic stability of a rumor-endemic equilibrium is provided. The influence of the delays and the saturation effects on the dynamics of the model is made clear through simulation experiments. In particular, it is found that (a) extended time delays lead to slower change in the number of spreaders or stiflers and (b) lifted saturation coefficients lead to slower change in the number of spreaders or stiflers. This work helps to deepen the understanding of complex rumor spreading phenomenon and develop effective rumor-containing schemes.

Distributed Resilient Nash Equilibrium Seeking for Aggregative Games of Second‐Order Systems Under Dos Attacks

2025-06-18

Shuicheng Yan , Peng Yi , Siliang Cheng +1 more | International Journal of Robust and Nonlinear Control

ABSTRACT This paper investigates the distributed Nash equilibrium seeking problem for aggregative games over a second‐order multi‐agent network subject to denial‐of‐service (DoS) attacks. To solve this problem, a novel distributed … ABSTRACT This paper investigates the distributed Nash equilibrium seeking problem for aggregative games over a second‐order multi‐agent network subject to denial‐of‐service (DoS) attacks. To solve this problem, a novel distributed algorithm is designed based on state estimation and adaptive gains, where each player can estimate the information of other nodes under DoS attacks. Then, the convergence of this algorithm is analyzed by the Lyapunov method and switched system theory. Furthermore, this algorithm overcomes the challenge caused by time‐varying topologies resulting from DoS attacks. Finally, a simulation example is presented to confirm the validity and correctness of the distributed algorithm designed in this paper.

Global Stability and Permanence of a Discrete-Time Two-Predators One-Prey System with Holling Type-III Response

2025-06-17

Xiongxiong Du , Xiaoling Han | Qualitative Theory of Dynamical Systems

Strong waves for epidemic model with time-space delay and multiple infectious stages

2025-06-17

Wenhui Zhang , Qiaoling Chen , Weixin Wu | Applicable Analysis

On a reaction–diffusion system modeling strong competition between two mosquito populations

2025-06-17

Nicolas Vauchelet | Bollettino dell Unione Matematica Italiana

Global Stability and Sensitivity Analysis of SIAR Model with Influenza A (H1N1)

2025-06-17

A. Sirijampa , Chukiat Saksurakan , Sutawas Janreung | Malaysian Journal of Mathematical Sciences

The SIAR model with symptomatic and asymptomatic individuals is introduced. The stability of equilibrium points are analyzed with the basic reproduction number (R0). The Disease-Free Equilibrium (DFE) is globally stable … The SIAR model with symptomatic and asymptomatic individuals is introduced. The stability of equilibrium points are analyzed with the basic reproduction number (R0). The Disease-Free Equilibrium (DFE) is globally stable when R0 < 1, and the Endemic Equilibrium (EE) is locally asymptotically stable when R0 > 1. For case α = 0, the global stability of EE is analyzed by using a geometric approach for the global stability. The Sensitivity Analysis (SA) of R0 and EE with parameters of influenza A (H1N1) are presented. The most sensitive parameter for R0 is the transmission rate to symptomatic infected individuals. The sensitivity of EE shows that the recovery rate of symptomatic and asymptomatic individuals have an effect on reducing patients when the recovery rate are increased. Therefore, controlling the spread of disease and reducing the treatment time can reduce the number of infected individuals. Simulations results by using numerical method are used to confirm the stability of the model. Further, this model is applied to predict the trend of influenza A cases of (H1N1) in Thailand during 2016 − 2022.

Chaos Control and Bifurcations in a Modified Discrete Prey–Predator Model with Weak Multiple Allee Effect

2025-06-17

Fi̇gen Kangalgi̇l , Meltem Altunkaynak | International Journal of Bifurcation and Chaos

This study explores the local dynamics of a discrete-time prey–predator model, which has been modified to include a weak multiple Allee effect on the prey population. The investigation encompasses topological … This study explores the local dynamics of a discrete-time prey–predator model, which has been modified to include a weak multiple Allee effect on the prey population. The investigation encompasses topological categorization, bifurcation analysis, and chaos control. The analysis reveals that the model exhibits flip bifurcation and Neimark–Sacker bifurcation within a narrow vicinity of the coexistence equilibrium point, as demonstrated through bifurcation theory. Furthermore, the direction of these bifurcations is elucidated. To stabilize chaos resulting from the bifurcation, the OGY method is employed. Numerical simulations are conducted to validate the theoretical findings, with maximum Lyapunov exponents indicating the probability of chaos in the model.

Prescribed Time Convergence Analysis for Continuous Action Iterated Dilemma with Lyapunov Stability Theory

2025-06-17

Syed Muhammad Amrr , Mohamed Zaery , S. M. Suhail Hussain +1 more | Dynamic Games and Applications

Propagation dynamics of a nonautonomous epidemic system with nonlocal diffusion

2025-06-16

Xiongxiong Bao , Zhucheng Jin | Journal of Differential Equations

On a FitzHugh–Nagumo nonlinear system with exponential growth

2025-06-16

João P. S. Maurício de Carvalho , Marco Túlio Furtado , Thainá Rodrigues de Melo | Milan Journal of Mathematics

Traveling waves for a general diffusive virus infection model with both virus-to-cell and cell-to-cell transmissions and adaptive immunity

2025-06-15

Séverin Foko , Chuene Thama Duba , Calvin Tadmon +1 more | Zeitschrift für angewandte Mathematik und Physik

Abstract The main purpose of this work is to investigate the existence and nonexistence of traveling waves for a virus infection model with adaptive immunity, virus-to-cell infection and cell-to-cell transmission. … Abstract The main purpose of this work is to investigate the existence and nonexistence of traveling waves for a virus infection model with adaptive immunity, virus-to-cell infection and cell-to-cell transmission. The virus-to-cell and cell-to-cell incidence rates are modeled by general nonlinear functions. The basic reproduction numbers are calculated for virus infection, antibody immune response, cytotoxic T lymphocytes (CTL) immune response, CTL immune competition, and antibody immune competition. By introducing an auxiliary nonlinear differential system and applying the Schauder’s fixed point theorem, combined with the method of upper-lower solutions, we prove the existence of traveling waves dependent not only on the five reproduction numbers but also on the critical wave speed. Moreover, we show that these traveling waves connect the infection-free equilibrium to each of the other four equilibria, namely the immune-free infection equilibrium, the infection equilibrium with only antibody immune defense, the infection equilibrium with only CTL immune response and the CTL-antibody-present infection equilibrium. Finally, an application is provided and some numerical simulations are performed to illustrate the theoretical results obtained.

Dynamic analysis of predator–prey model with fear, cannibalism, and prey immigration using caputo and ABC fractional derivatives

2025-06-14

Lei Yang , Wei Feng , Minxuan Zhang +1 more | Indian Journal of Physics

Non-periodic intermittent stochastic control for SVIQR epidemic model on complex network with saturation incidence rate

2025-06-13

Xinjie Fu , JinRong Wang | Chaos Solitons & Fractals

Asymptotic Behavior of Fractional‐Order Holling Type II Prey‐Predator With Hunting Cooperation

2025-06-12

M. Sivaranjani , M. Sambath | Mathematical Methods in the Applied Sciences

ABSTRACT In this paper, we developed a fractional‐order one‐prey two‐predator system considering Holling type II functional response and hunting cooperation. We also investigated the interspecific dynamics of prey between the … ABSTRACT In this paper, we developed a fractional‐order one‐prey two‐predator system considering Holling type II functional response and hunting cooperation. We also investigated the interspecific dynamics of prey between the I predator and the II predator. We also proved the boundedness, positivity, the uniqueness, and the existence of the solutions of our system. In addition, we showed the local stability and the global stability behavior of the equilibria, and a Hopf bifurcation occurred. Also, we computed the numerical simulations of the solutions to demonstrate the consistency of the analytical approach, in which the theoretical observations are confirmed by the trajectories and phase portraits finally. It is observed that our system is impacted by hunting cooperation, and the fractional‐order derivative stabilizes the system.

A Piecewise-Smooth Dynamic System with Two Thresholds and Its Application to Epidemic Control

2025-06-12

Haifeng Wang , Yanni Xiao | International Journal of Bifurcation and Chaos

A general type of piecewise-smooth dynamic system with two thresholds is analyzed in this work. We define some fundamental notions for the proposed system such as oscillating space and real/virtual … A general type of piecewise-smooth dynamic system with two thresholds is analyzed in this work. We define some fundamental notions for the proposed system such as oscillating space and real/virtual equilibrium, which generalizes the counterparts for the planar Filippov system. Moreover, we show that under certain conditions the planar switched system with two thresholds generates a novel limit cycle, and analyze the properties of this periodic solution such as existence, stability, amplitude and period. Interestingly, the existence and stability of this periodic solution in the oscillating space are consistent with the pseudo-equilibrium of the corresponding planar Filippov system. Hence, we establish the connection between the planar switched system with two thresholds and the planar Filippov system. Finally, we apply the modeling and analytical approaches to a piecewise-smooth epidemic model with density-dependent interventions, describing the control measure that is triggered when the number of infected individuals increases and reaches a critical level while being suspended when it decreases down to another level. We prove that the epidemic model stabilizes at either the endemic equilibrium of the free system (the one not under control) or the new periodic solution induced by the two thresholds, depending on the threshold levels. The two-threshold measure is able to suppress the number of infected individuals during the evolution of an infectious disease.

Periodic bistable traveling waves for a nonlocal dispersal competition system with seasonal succession

2025-06-12

Junrui Wang , Guo‐Bao Zhang | International Journal of Biomathematics

Stability and bifurcation of a predator–prey model with variable search rate in advective environments

2025-06-12

Quan Qian , Weihua Jiang , Xun Cao | Nonlinear Analysis Real World Applications

Stability analysis of a delay logistic growth model with nonlinear harvesting

2025-06-12

Martin Anokye , Sampson Z. Nkangbi , Agnes Adom-Konadu +4 more | Quality & Quantity

Spatiotemporal dynamics of a food chain model incorporating higher-order interactions and slow–fast effect

2025-06-12

Min Feng , Min Xiao , Jinde Cao +3 more | Chaos Solitons & Fractals

Averaging result for impulsive 𝜓-Hilfer fractional stochastic pantograph-type delay system driven by Poisson jumps

2025-06-12

A. Jalisraj , R. Udhayakumar | Random Operators and Stochastic Equations

Abstract This article explores the averaging principle for 𝜓-Hilfer fractional neutral impulsive stochastic differential equations with pantograph-type delay driven by Poisson jumps. With the help of the Khasḿinskii approach, we … Abstract This article explores the averaging principle for 𝜓-Hilfer fractional neutral impulsive stochastic differential equations with pantograph-type delay driven by Poisson jumps. With the help of the Khasḿinskii approach, we approximate the nonautonomous 𝜓-Hilfer fractional stochastic differential equations with both deterministic and stochastic jumps by an autonomous 𝜓-Hilfer fractional stochastic differential equations without deterministic jumps and to demonstrate the convergence in <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi>L</m:mi> <m:mi mathvariant="monospace">p</m:mi> </m:msup> </m:math> L^{\mathtt{p}} sense. Using Lipschitz and growth conditions and elementary inequalities, assumptions are made. With the help of Jensen’s inequality, Burkholder–Davis–Gundy inequality, Hölder inequality, Doob’s martingale inequality, Kunitha’s inequality and Gronwall–Bellman’s inequality, an averaging principle of our proposed system is obtained in the sense of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:msup> <m:mi mathvariant="monospace">L</m:mi> <m:mi mathvariant="monospace">p</m:mi> </m:msup> </m:math> \mathtt{L^{p}} convergence. An illustration is given to support the theoretical results.

A nontrivial beneficial aspect of predation-driven Allee effect in an eco-epidemiological model

2025-06-12

Kaushik Kayal , Sudip Samanta , Joydev Chattopadhyay | The European Physical Journal Plus

Interplay between preys’ anti-predator behavior and predators’ cooperative hunting: A mathematical approach

2025-06-12

Yilin Zhang , Lijuan Chen , Fengde Chen +1 more | Chaos Solitons & Fractals

Complexity and chaos of a time-fractional SAIR epidemic system with respect to fractional order

2025-06-10

Zhen Wang , Gongsheng Li | Physica Scripta

Abstract This article deals with complexity and chaos with respect to the fractional order in a fractional-order SAIR epidemic system by mathematical analysis and numerical simulations. By directly choosing a … Abstract This article deals with complexity and chaos with respect to the fractional order in a fractional-order SAIR epidemic system by mathematical analysis and numerical simulations. By directly choosing a power-law survival function, the fractional-order SAIR system according with physical law is proposed based on non-Markovian process. The asymptotic solution of the system in the form of series is derived by the Laplace-Adomian decomposition method (Laplace-ADM), and its convergence is proved. Numerical simulations are performed based on the asymptotic solution, and the dynamics and chaos of the dynamic system with respect to the fractional order are analyzed and illustrated in terms of the maximum Lyapunov exponent and structural complexity. By employing the real data of COVID-2019 in the US during April and May in 2020, the fractional-order SAIR model is applied to explain and predict the transmission of the infectious disease by using the parameter identification and the differential evolution algorithm.