Disease In Prey Research Articles

Numerical Study of the Reaction Diffusion Prey–Predator Model Having Holling II Increasing Function in the Predator Under Noisy Environment

The current study deals with the stochastic diffusive prey–predator model with Holling II increasing function in the predator. As it is a population dynamics its population can be affected by various factors such as disease in prey–predator species, environmental fluctuation, etc. So, the underlying model is considered under the impact of a temporal multiplicative noise. The numerical solution of the governing model is obtained by finite difference schemes. To check the accuracy of the numerical solution, the stability and consistency of the schemes in the mean square sense are derived. All the schemes are consistent with the model and von Neumann stable. Several simulations are drawn to check the efficacy of the scheme. A test problem is investigated with numerical schemes and for the different values of the parameters, 3D and 2D plots are drawn. A graphical representation of the given system is drawn which shows the behavior of both species and the efficiency of the novel schemes. Hope so, these results will motivate the researcher to consider the stochastic prey–predator model for a better understanding of the ecosystem.

Dynamical analysis of a modified Leslie–Gower predator–prey model with disease in prey incorporating a prey refuge and treatment

In this paper, we present and assess a predator–prey Leslie–Gower model including disease, refuge and treatment in prey population. There are two groups of prey: those who are susceptible and infected. It is hypothesized that prey population is affected by diseases and refuge, and grows logistically in the absence of predators. Infected prey population receives treatment. The predators’ growth rate is governed by the modified Leslie–Gower dynamics. The dynamical attributes of the resulting system are boundedness, positivity of solutions, extinction criteria, existence and (local and global) stability. Biology uses mathematical analysis to identify the possible attributes of equilibrium points. The focus of this study is to assess how treatment and refuge affect the populations of ill prey, susceptible prey, predators and treated prey. The numerical simulation indicates that the influence of treatment, and refuge change the dynamics of the system (2.1). Extensive numerical simulations were performed to validate our analytical findings by using the Mathematica and MATLAB software.

Deterministic vs. stochastic dynamics of a predator–prey system with disease in prey: Impact of fear and supplementary foods

In this study, we delve into the dynamics of a generalist predator–prey system with prevalence of a disease in the prey population and the presence of predator-induced fear. In this intricate ecological web, the fear response triggered by predators influences the birth rate of susceptible prey population and also escalates intra-specific competition among them. In an effort to encapsulate a more realistic scenario, we extend our deterministic model to its stochastic counterpart by introducing environmental white noise that impacts the mortality rates of both prey and predator species. Comprehensive mathematical analyses are performed on both the deterministic and stochastic systems to elucidate their qualitative behaviors. Specifically, we derive conditions under which the stochastic system exhibits a unique global positive solution and explore the potential extinction of species within the ecosystem. To unravel the intricate dynamics numerically, we perform sensitivity of parameters, and construct one- and two-parameter bifurcation diagrams. Our investigations reveal that when the costs of fear surpass specific thresholds and disease incidence is high, both the susceptible and infected prey populations face extinction. Notably, the introduction of supplementary foods can lead to system’s destabilization, potentially pushing it towards a state where only predators can persist. Moreover, we observe that lower intensities of white noise have minimal impact on the system’s dynamics, while higher noise intensities introduce substantial fluctuations and may precipitate the extinction of species within the ecosystem. Furthermore, we elucidate the abundances of prey and predator species within the ecosystem through histogram plots.

Dynamics of a Delayed Fractional-Order Predator–Prey Model with Cannibalism and Disease in Prey

In this study, a class of delayed fractional-order predation models with disease and cannibalism in the prey was studied. In addition, we considered the prey stage structure and the refuge effect. A Holling type-II functional response function was used to describe predator–prey interactions. First, the existence and uniform boundedness of the solutions of the systems without delay were proven. The local stability of the equilibrium point was also analyzed. Second, we used the digestion delay of predators as a bifurcation parameter to determine the conditions under which Hopf bifurcation occurs. Finally, a numerical simulation was performed to validate the obtained results. Numerical simulations have shown that cannibalism contributes to the elimination of disease in diseased prey populations. In addition, the size of the bifurcation point τ0 decreased with an increase in the fractional order, and this had a significant effect on the stability of the system.

Direction and stability of Hopf bifurcation in an eco-epidemic model with disease in prey and predator gestation delay using Crowley-Martin functional response

<p>In this work, we have studied an eco-epidemic model using the Crowley-Martin functional response that includes disease in prey and gestation delay in the predator population. The model possesses three equilibria, namely the disease-free, Predator-free, and the interior equilibrium point. In addition, we examined the stability of the equilibrium points varying the infection rate and time delay parameter. Detailed analysis of Hopf bifurcation of the interior equilibrium point contains two situations: with delay and without delay. Moreover, we have studied the direction of the Hopf bifurcation and the stability of periodic solutions utilizing normal form theory and the center manifold theorem. It is emphasized that Hopf bifurcation occurs when the time delay exceeds the critical value and that the critical value of the delay is strongly impacted by the infection rate in prey. A detailed numerical simulation is provided to verify the analytical results.</p>

ROLE OF SPACE IN AN ECO-EPIDEMIC PREDATOR-PREY SYSTEM WITH THE EFFECT OF FEAR AND SELECTIVE PREDATION

In ecological systems, the fear of predation risk asserts a privilege to the prey species by restricting their exposure to the potential predators. It also imposes costs by constraining the exploration of optimal resources. Additional foods for predators play a pivotal role in the biological conservation programs. The predators have ability to distinguish between the susceptible and infected prey items, and they avoid the latter ones to reduce their fitness cost. A predator-prey model with disease in prey is investigated in this study with an aim to explore the effects of fear factor, additional foods and selective predation on the ecological systems. We also investigate the spatio-temporal model to incorporate the facts that the prey and predator populations perform active movements in the spatial directions for their biological relevance. Both the temporal and spatio-temporal models are analyzed through noteworthy mathematical as well as numerical techniques. Our simulation results show that the level of fear responsible for the reduction in the birth rate of susceptible prey, rate of disease transmission and the selective feeding behavior of predators have potentials to create instability in the ecosystem. In contrast, the level of fear responsible for reduction in the disease prevalence can restore stability in the ecosystem by killing the persistent oscillations. Our eco-epidemic system exhibits chaotic nature if the growth of predators due to additional food sources is very low. We find that the spatio-temporal model demonstrates different spatial patterns of the prey and predator populations in the ecosystem.

Stability Analysis of a Fractional Order Prey-Predator Model with Disease in Prey

Stability Analysis of a Fractional Order Prey-Predator Model with Disease in Prey

Stationary distribution and global stability of stochastic predator-prey model with disease in prey population

In this paper, a new stochastic four-species predator-prey model with disease in the first prey is proposed and studied. First, we present the stochastic model with some biological assumptions and establish the existence of globally positive solutions. Moreover, a condition for species to be permanent and extinction is provided. The above properties can help to save the dangered population in the ecosystem. Through Lyapunov functions, we discuss the asymptotic stability of a positive equilibrium solution for our model. Furthermore, it is also shown that the system has a stationary distribution and indicating the existence of a stable biotic community. Finally, our results of the proposed model have revealed the effect of random fluctuations on the four species ecosystem when adding the alternative food sources for the predator population. To illustrate our theoretical findings, some numerical simulations are presented.

Dynamics of predator-dependent nonlinear disease transmission in infected prey with diverse functional response

The disease in prey causes the indirect effect on the disease transmission of prey-predator interactions; this phenomenon of predator-dependent disease transmission scenario can arise as a consequence of anti-predator defence behaviour, debilitating the immune system of the prey. This concept is implemented in the proposed nonlinear mathematical prey-predator model, where an infectious disease infects only prey populations. The interaction between the susceptible prey and predator is assumed to be governed by Crowley-Martin type functional response and Holling I type functional response for the predation of infected prey. The susceptible prey becomes infected when contact occurs with the infected prey. The existence, uniqueness, boundedness, and feasibility and stability conditions of the fixed points of the system are analyzed. Hopf bifurcation analysis for the system is perceived and presented through bifurcation diagrams for different parameter values. Lastly, numerical exercises and graphical demonstrations are given to help our investigative findings.

An eco-epidemiological model with the impact of fear.

In this study, we propose and analyze an eco-epidemiological model with disease in prey and incorporated the effect of fear on prey species due to predator population. We assume that the prey population grows logistically in the absence of predator species, and the disease is limited to the prey population only. We divide the total prey population into two distinct classes: susceptible prey and infected prey. Predator populations are not infected by the diseases, though feed both the susceptible and infected prey. Due to the fear of predators, the prey population becomes more vigilant and moves away from suspected predators. Such a foraging activity of prey reduces the chance of infection among susceptible prey by lowering the contact with infected prey. We assume that the fear of predators has no effect on infected prey as they are more vigilant. Positivity, boundedness, and uniform persistence of the proposed model are investigated. The biologically feasible equilibrium points and their stability are analyzed. We establish the conditions for the Hopf bifurcation of the proposed model around the endemic steady state. As the level of fear increases, the system moves toward the steady state from a limit cycle oscillation. The increasing level of fear cannot wipe out the diseases from the system, but the amplitude of the infected prey decreases as the level of fear is increased. The system changes its stability as the rate of infection increases, and the predator becomes extinct when the rate of infection in prey is high enough though predators are not infected by the disease.

Study of Dynamical Behavior of a Delayed Stage-Structured Predator-Prey Model with Disease in Prey

The present paper deals with the dynamics of a stage-structured predator-prey model, with a ratio-dependent functional response including gestational delay in the predator. The prey is carrying an infection which affects the predator adversely. The boundedness of solutions and the stability of equilibrium points have been investigated. There is a Hopf-bifurcation arising out of the variation in the time-delay parameter. Numerical simulations of phase-plane diagrams, and bifurcation diagrams illustrate the dependence of the system on the delay -time. The effect of the disease transmission from prey to predator has also been illustrated through simulations.

Modelling the role of predation on disease burdens of prey.

Research Highlight: Brandell, E. E., Cross, P. C., Smith, D. W., Rogers, W., Galloway, N. L., MacNulty, D. R., Stahler, D. R., Treanor, J. & Hudson, P. J. (2022). Examination of the interaction between age-specific predation and chronic disease in the Greater Yellowstone Ecosystem. Journal of Animal Ecology, 00, 1-12. https://doi.org/10.1111/1365-2656.13661. Predation can alter disease dynamics in prey. If predators select for infected individuals, they can reduce disease burdens. In other cases, predators can increase disease burdens via various mechanisms such as altered prey behaviour. The influence of predation on disease dynamics is a result of interactions among various traits of the predators, prey and the pathogen itself. For example, pathogens tend to vary with age and predators typically select for certain age classes. Thus, the overlap between ages selected by predators and those infected will likely contribute to any effects of predation on reducing disease burdens. In this paper, Brandell et al. (2022) develop a model to evaluate the predator cleansing effect given age-based variation in pathogens and predation. The model was developed for Chronic Wasting Disease (CWD) infections in deer and elk facing predation by cougars and grey wolves in the Greater Yellowstone Ecosystem. The results indicate that predators can reduce CWD outbreak size, especially if selecting for infected individuals. CWD is an always fatal disease and this work suggests that predators could reduce disease burdens in cervids. The model is also applicable to other systems and promises to further our understanding of the role of predation on disease in prey, as well as drive future empirical studies.

A Delayed Eco-Epidemiological Model with Weak Allee Effect and Disease in Prey

In this paper, we have proposed and analyzed a mathematical model for the eco-epidemiological system with disease in prey population, placing particular emphasis on the effects of an incubation time delay and the influence of weak Allee effect on the growth of the predator population. We investigate basic properties of the proposed model including positivity, boundedness, uniform persistence and the stability of the biologically feasible equilibrium points. Using the time delay as bifurcation parameter, we explore the stability of the interior equilibrium point and observe that Hopf bifurcation can occur when the incubation time delay crosses some threshold value. We have identified the stability regions associated with the extinction of populations, stability of the steady states, and high-periodic oscillations in disease transmission. Analytical findings are supported by numerical illustrations that demonstrate the behavior of the proposed model in different dynamical regimes. Stability criteria for the biologically feasible equilibrium points were obtained and validated with numerical simulations. We found most sensitive system parameters using the PRCC sensitivity analysis. We observe that our model simulation exhibits high-periodic oscillations due to the increasing value of time delay parameter [Formula: see text] and the disease transmission rate [Formula: see text].

A study on eco-epidemiological model with fractional operators

This paper employs fractional calculus (FC) for modeling three-dimensional prey-predator populations model. This study uses an eco-epidemiological system in which the prey disease is constructed as a susceptible-infected (SI) disease. The Caputo and Caputo-Fabrizio (CF) operators are consolidated into this model and the existence of a solution is explored. The model is evaluated for uniqueness under what conditions it provides a unique solution. Based on the singular kernel of the Caputo operator, we investigate the properties of the proposed model and show it can be stable locally. We developed maximum bifurcation diagrams to analyze the dynamics of the epidemiological model as varying transmission rates β and attack rates b1. To simulate the dynamics of proposed fractional systems, we employed the Toufik-Atangana (TA) numerical technique with the Caputo operator. Moreover, we present another numerical approach based on Adams-Bashforth (AB) technique with CF operators. Results of the numerical analysis show that diverse non-integer operator alternatives to the eco-epidemiological predator-prey model result in a range of dynamical behaviors.

The The Dynamics of a Prey-Predator Model with Infectious Disease in Prey: Role of Media Coverage

In this paper, an eco-epidemiological model with media coverage effect is proposed and studied. A prey-predator model with modified Leslie-Gower and functional response is studied. An -type of disease in prey is considered. The existence, uniqueness and boundedness of the solution of the model are discussed. The local and global stability of this system are carried out. The conditions for the persistence of all species are established. The local bifurcation in the model is studied. Finally, numerical simulations are conducted to illustrate the analytical results.

Analysis on stochastic predator-prey model with distributed delay

Abstract In the present work, we consider a stochastic predator-prey model with disease in prey and distributed delay. Firstly, we establish sufficient conditions for the extinction of the disease and also permanence of healthy prey and predator. Besides, we obtain the condition for the existence of an ergodic stationary distribution through the stochastic Lyapunov function. Finally, we provide some numerical simulations to validate our theoretical findings.

Dynamical analysis of polluted prey-predator system with infected prey

In this paper, a prey-predator model in polluted environment with disease in prey has been proposed and studied. It is assumed that only prey population is prone to disease whereas, both the populations are affected by the pollutant. Boundedness of the solution of the system is discussed. Existence of all possible equilibrium points has been established. Using Routh Hurwitz criterion, local stability of all the possible equilibrium points has been obtained. Also, interior equilibrium point has been proved to be globally asymptotically stable using Lyapunov function. Then time delay has been introduced in the system making the model more realistic. Existence and direction of Hopf bifurcation in the delay model has been established using normal form theory and center manifold theorem. By taking a set of hypothetical and biologically feasible parameters, model has been studied numerically using MATLAB and the effect of pollutant on the system has been deduced.

A prey–predator system with disease in prey and cooperative hunting strategy in predator

A predator–prey model is proposed in this work where the prey population is infected by a disease. Here, healthy prey species show defence mechanism while they are attacked by the predator. Moreover as the infected prey are already physically weak, so, predator apply cooperative hunting strategy while consume infected prey to get more food. It helps the predator population to grow with a higher rate. But calculation gives that if they start to hunt the infected prey with a larger cooperative hunting rate, then ultimately predator population decrease with time. Boundedness and positivity of the system variables show that the proposed model system is well-posed. Routh–Hurwitz criterion provides the local stability conditions of the equilibrium points. Also, the system becomes permanent under certain parametric restrictions. The numerical results, verified using MATLAB, support the analytical findings. Numerical simulations give that the parameter denoting cooperative hunting rate can change the system dynamics and we can get oscillating behaviour by regulating this parameter. Moreover transcritical and saddle-node bifurcations occur by regulating the death rate of predator around the critical points. Occurrence of Bogdanov–Takens, generalized Hopf and Cusp bifurcations have also been observed here.

Optimal control problem for a general reaction-diffusion eco-epidemiological model with disease in prey

This paper deals with an optimal control problem for a general reaction-diffusion predator-prey model with disease in prey population. Infected prey will recover from a medication considered as a control strategy. Our primary goal is to characterize an optimal control which minimizes the total density of infected prey and the costs of treatment. Firstly, we obtain the existence and some estimates of the unique strong solution for the controlled system by applying semigroup theory. Subsequently, the existence of optimal pair is proved by means of the technique of minimizing sequence. Furthermore, by proving the differentiability of the control-to-state mapping, we derive the first-order necessary optimality condition, and point out that the optimal is a Bang-Bang control in a special case. Finally, several numerical simulations are performed to illustrate the concrete realization and practical application of the theoretical results obtained in this contribution.

Analisis Kestabilan Model Predator-Prey dengan Infeksi Penyakit pada Prey dan Pemanenan Proporsional pada Predator

The dynamics of predator-prey model with infectious disease in prey and harvesting in predator is studied. Prey is divided into two compartments i.e the susceptible prey and the infected prey. This model has five equilibrium points namely the all population extinction point, the infected prey and predator extinction point, the infected prey extinction point, and the co-existence point. We show that all population extinction point is a saddle point and therefore this condition will never be attained, while the other equilibrium points are conditionally stable. In the end, to support analytical results, the numerical simulations are given by using the fourth-order Runge-Kutta method.