Disease In Prey Research Articles

A Prey-Predator Model with Michael Mentence Type of Predator Harvesting and Infectious Disease in Prey

A prey-predator model with Michael Mentence type of predator harvesting and infectious disease in prey is studied. The existence, uniqueness and boundedness of the solution of the model are investigated. The dynamical behavior of the system is studied locally as well as globally. The persistence conditions of the system are established. Local bifurcation near each of the equilibrium points is investigated. Finally, numerical simulations are given to show our obtained analytical results.

Mathematical analysis of an optimal control problem for the predator‐prey model with disease in prey

SummaryThis article deals with an optimal control problem governed by a system that models the dynamics of predator‐prey interactions. We study the minimization of the infective prey density. Furthermore, our purpose is here to establish the existence of weak solutions and derive some optimality conditions. Finally, the impact of the control terms are studied to get an insight of the predator‐prey model adopting various numerical simulations.

The Dynamics of an Eco-Epidemiological Model with Allee Effect and Harvesting in the Predator

The aim of this study was to propose and evaluate an eco-epidemiological model with Allee effect and nonlinear harvesting in predators. It was assumed that there is an SI-type of disease in prey, and only portion of the prey would be attacked by the predator due to the fleeing of the remainder of the prey to a safe area. It was also assumed that the predator consumed the prey according to modified Holling type-II functional response. All possible equilibrium points were determined, and the local and global stabilities were investigated. The possibility of occurrence of local bifurcation was also studied. Numerical simulation was used to further evaluate the global dynamics and the effects of varying parameters on the asymptotic behavior of the system.

Chaos in a nonautonomous eco-epidemiological model with delay

In this paper, we propose and analyze a nonautonomous predator-prey model with disease in prey, and a discrete time delay for the incubation period in disease transmission. Employing the theory of differential inequalities, we find sufficient conditions for the permanence of the system. Further, we use Lyapunov’s functional method to obtain sufficient conditions for global asymptotic stability of the system. We observe that the permanence of the system is unaffected due to presence of incubation delay. However, incubation delay affects the global stability of the positive periodic solution of the system. To reinforce the analytical results and to get more insight into the system’s behavior, we perform some numerical simulations of the autonomous and nonautonomous systems with and without time delay. We observe that for the gradual increase in the magnitude of incubation delay, the autonomous system develops limit cycle oscillation through a Hopf-bifurcation while the corresponding nonautonomous system shows chaotic dynamics through quasi-periodic oscillations. We apply basic tools of non-linear dynamics such as Poincaré section and maximum Lyapunov exponent to confirm the chaotic behavior of the system.

The Dynamics and Analysis of Stage-Structured Predator-Prey Model With Prey Refuge and Harvesting Involving Disease in Prey Population

In this paper, a mathematical model consisting of the prey-predator model with SI infectious disease in prey is proposed and analyzed. The model includes harvesting on the infected prey population, it is assume that the disease is not transmitted from prey to predator. In addition, the disease spread by contact between susceptible individuals and infected individuals, the mature predator only can predate the susceptible and infected prey which are outside refuge according to Lotka-Volterra type of functional response. While, the immature predator depends completely in it’s feeding on the mature predator. The existence, uniqueness and boundedness of the solution are discussed. The stability analysis of all possible equilibrium points is studied. Also, Lyapunove function is used to study the global dynamics of the model. Further, the effect of the disease, refuge and harvest on the dynamical of the system is discussed using numerical simulation.

Multiple bifurcations analysis in a delayed predator–prey system with disease in prey and stage structure for predator

In this paper, a delayed eco-epidemiological model with disease in prey, anti-predator factor for the prey and stage structure for the predator is proposed. The conditions for the stability and coexistence of the populations have been derived. Positivity and boundedness of all solutions with positive initial conditions has been proved. Sufficient conditions for the occurrence of several Hopf and Bogdanov–Takens bifurcations about the endemic steady state are derived. By taking the delay as the bifurcation parameter, it is shown that Hopf and Bogdanov–Takens bifurcations occur at positive steady state for some critical values of the delay. The normal form of the Bogdanov–Takens singularity is obtained by performing a center manifold reduction and by using the normal form theory of FDEs. Some numerical simulations of solutions in different parametric regions illustrating Hopf and homoclinic bifutcations are given to support the analytical results.

Role of harvesting in controlling chaos and disease propagation in predator-prey system with disease in prey

The paper explores an eco-epidemiological model with harvesting in the species and the disease is circulating in the prey population. The curiosity of this paper is to consider the role of harvesting on chaotic dynamics. We perform the local and global stability analysis of the equilibrium points and the Hopf bifurcation analysis around the interior equilibrium point. Further we pay attention to the direction of Hopf Bifurcation. Our numerical simulations reveal that the three species eco-epidemiological system shows chaos in low level of infection. It is observed that when force of infection increases chaos becomes stable. We conclude that chaotic dynamics can be controlled by the harvesting parameter as well as the force of infection.We apply basic tools of non-linear dynamics such as Poincare section and maximum Lyapunov exponent to identify chaotic behaviour of the system.

Analysis of a predator–prey model with herd behavior and disease in prey incorporating prey refuge

In this work, we have introduced an eco-epidemiological model of an infected predator–prey system. Incorporation of prey refuge gives that a fraction of the infected prey is available to the predator for consumption. Moreover, to make the model more realistic to the environment, we have introduced strong Allee effect in the susceptible population. Boundedness and positivity of the solution have been established. Local stability conditions of the equilibrium points have been found with the help of Routh–Hurwitz criterion and it has been observed that if a prey population is infected with a lethal disease, then both the prey (susceptible and infected) and predator cannot survive simultaneously in the system for any parametric values. The disease transmission rate and the attack rate on the susceptible have an important role to control the system dynamics. For different values of these two key parameters, we have got only healthy or disease-free or predation-free or a fluctuating disease-free or even a fluctuating predator-free system with some certain parametric conditions.

A Michaelis–Menten Predator–Prey Model with Strong Allee Effect and Disease in Prey Incorporating Prey Refuge

Here, we have proposed a predator–prey model with Michaelis–Menten functional response and divided the prey population in two subpopulations: susceptible and infected prey. Refuge has been incorporated in infected preys, i.e. not the whole but only a fraction of the infected is available to the predator for consumption. Moreover, multiplicative Allee effect has been introduced only in susceptible population to make our model more realistic to environment. Boundedness and positivity have been checked to ensure that the eco-epidemiological model is well-behaved. Stability has been analyzed for all the equilibrium points. Routh–Hurwitz criterion provides the conditions for local stability while on the other hand, Bendixson–Dulac theorem and Lyapunov LaSalle theorem guarantee the global stability of the equilibrium points. Also, the analytical results have been verified numerically by using MATLAB. We have obtained the conditions for the existence of limit cycle in the system through Hopf Bifurcation theorem making the refuge parameter as the bifurcating parameter. In addition, the existence of transcritical bifurcations and saddle-node bifurcation have also been observed by making different parameters as bifurcating parameters around the critical points.

A non-autonomous predator-prey model with infected prey

A non-constant eco-epidemiological model with SIS-type infectious disease in prey is formulated and investigated, it is assumed that the disease is endemic in prey before the invasion of predator and that predation is more likely on infected prey than on the uninfected. Sufficient conditions for both permanence and extinction of the infected prey, and the necessary conditions for the permanence of the infected prey are established. It is shown that the predation preference to infected prey may even increase the possibility of disease endemic, and that the introduction of new resource for predator could be helpful for it to eradicate the infected prey. Numerical simulations have been performed to verify/extend our analytical results.

Analysis of a nonautonomous eco‐epidemic diffusive model with disease in the prey

This paper deals with the behavior of positive solutions to a nonautonomous reaction‐diffusion system with homogeneous Neumann boundary conditions, which describes a two‐species predator‐prey system in which there is an infectious disease in prey. The sufficient condition on the permanence of the prey and the predator is established by combining the comparison principle with the results related to the corresponding ODE system. Some sufficient conditions for the spreading and vanishing of the disease are obtained. The global attractivity is also discussed by constructing a Lyapunov functional. Our results show that the disease is spreading if the transmission rate is suitably large, while if the transmission rate is small, the disease must be vanishing.

CHAOTIC EFFECTS ON DISEASE SPREAD IN A SIMPLE ECO-EPIDEMIOLOGICAL SYSTEM

In this paper, an eco-epidemiological model where prey disease is structured as a susceptible-infected model is investigated. Thresholds that control disease spread and population persistence are obtained. Existence, stability and instability of the system are studied. Hopf bifurcation is shown to occur where a periodic solution bifurcates from the coexistence equilibrium. Simulations show that the system exhibits chaotic phenomena when the transmission rate is varied.

Dynamics of a prey-generalized predator system with disease in prey and gestation delay for predator

In the present study, a prey-generalized predator model is proposed with disease in the prey and gestation delay for predator. The asymptotic behavior of the model is studied for all the feasible equilibrium states. The criterion for local stability of the system are established around steady states and thresholds for Hopf bifurcation are determined at the endemic as well as disease-free state. The respective sensitive indices of the variables are identified at the endemic state by performing the sensitivity analysis. Further numerical simulations have been carried out to justify our analytic findings.

具有时滞的生态传染病系统的稳定性分析

本文考虑了疾病在食饵种群中传播和具有Holling II型功能反应的时滞生态系统，主要分析时滞对系统局部稳定性的影响。当时滞不存在时，系统在内部平衡点处是局部渐近稳定的；但随着时滞 τ 的逐渐增加并超过临界值时，系统由稳定状态变为不稳定且产生Hopf分支，从而得到了Hopf分支的存在条件，最后利用数值模拟来验证所得结论。这些结论预测了疾病在种群间的发展趋势，并为控制疾病在种群间传播提供了可靠的理论依据。 In this paper, a delayed eco-epidemiological system with a disease in prey is considered. Its dy-namics of stability and the effect of delay on this system have been studied. The system without delay is locally asymptotically stable at the internal equilibrium point. With the delay gradually increasing, the system will be unstable and occurHopf bifurcation. Finally, the numerical simula-tion is carried out to verify the conclusions. These results can predict the trend of the populations with disease, and provide a reliable theoretical basis for controlling the spread of disease in populations.

Mathematical modelling of prey-predator interaction with disease in prey

Mathematical modelling of prey-predator interaction with disease in prey

Mathematical modelling of prey-predator interaction with disease in prey

This paper presents a nonlinear mathematical model of prey-predator interaction in which the prey is infected by an infectious disease while assuming that the disease is not transmitted to predator though the rates of predation can be different for the susceptible and infected preys. We also assume that only susceptible prey population contributes in the reproduction. The infective population competes with susceptible population to population growth towards the carrying capacity and here the disease transmission follows the standard incidence. The basic reproduction numbers both in absence and presence of the predator are computed and the equilibria of the mathematical model are obtained. Our results show that there is a possibility of two coexistence equilibria for some set of parameters but only one of them can be locally asymptotically stable. We also observed that the system undergoes 'Hopf-bifurcation' when the maximum predation rate β crosses a threshold value. Finally, the numerical simulation is performed and that supports the analytical findings.

Predator–prey harvesting model with fatal disease in prey

A theoretical eco‐epidemiological model of a prey–predator interaction system with disease in prey species is studied. Predator consumes both susceptible and infected prey population, but predator also feeds preferentially on many numerous species, which are over represented in the predator's diet. Equilibrium points of the system are determined, and the dynamic behaviour of the system is investigated around equilibrium points. Death rate of predator species is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighbourhood of the coexisting equilibria. Numerical simulations are carried out to support the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.

Intra-specific competition in predator can promote the coexistence of an eco-epidemiological model with strong Allee effects in prey

An eco-epidemiological model with Allee effects and disease in prey has been proposed and analyzed. The proposed model incorporates intra-specific competition in predator due to the limited food source, and assumes standard incidence disease transmission. We analyzed the corresponding submodels with and without the Allee effects to obtain the complete dynamics of the full model. Our results show that our full model shows multi-stability between the planner equilibriums (where the susceptible prey co-exists with infected prey or predator); both the full model and its submodels exhibit the hydra effects caused by the intra-specific competition in predator. We determined the existence of multiple interior attractors and their stability. Our analysis shows that our system has at most two interior equilibria whose stability is either both saddle or one stable with another one saddle. One of the most interesting findings is that the competition in the predator can promote the coexistence of all the three populations. In addition, we discussed how the frequency-dependent transmission differs from the model with the density-dependent transmission and compare the hydra effects observed in our model to other existing models in literature.

A Study of a Prey-Predator System with Disease in Prey

A Study of a Prey-Predator System with Disease in Prey

A mathematical study of an eco-epidemiological system on disease persistence and extinction perspective

A prey–predator system with disease in prey is proposed. The proposed system is an extension of the model analyzed by Bhattacharyya and Mukhopadhyay (2011) which did not consider the density of fish population as a dynamic variable which significantly influence the dynamics of the system. The coexistence equilibria of the system is determined and the dynamic behavior of the system is investigated around coexistence equilibria. Incidence rate of the disease is considered as a bifurcation parameter to examine the occurrence of Hopf bifurcation in the neighborhood of the co-existing equilibria. Sufficient conditions are derived for the global stability of the system around coexistence equilibria. Uniform strong persistence of the system is discussed in order to ensure long-term survival of the species. The obtained results are useful to extract the criteria for disease extinction and persistence. Finally, some numerical simulations are given to verify the analytical results, and the system is analyzed through graphical illustrations.