Infected Prey Population Research Articles

On Stability Properties In Prey-Prodator Model With General Incidence

In this paper we consider a prey-predator systems that the susceptibleand infected prey population are predated by predator species .Also we discuss different models of prey-predator systems With general incidence H ( S,I)The aim of this paper is to study the dynamic of prey-predator model by different techniques with a generalized incidence .

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.

Mathematical Modeling of Infectious Disease and Prey-Predator Interaction with Optimal Control

In this paper, the impact of viral illnesses on the predator-prey relationship with an optimal control analysis is studied. An ecoepidemiological model of four compartments, namely, susceptible prey, susceptible predator, infected prey, and infected predator populations, in the interaction of the prey-predator system is formulated. The fundamental tenet of our ecoepidemiology model is that sick predators do not engage in predation. It is confirmed that the system’s solution exists, is positive, and is bounded. The system’s equilibrium points are determined and computed. Lyapunov functions and a linearizing form are used for local and global stability analysis, respectively. The next generation matrix approach is used to calculate the threshold value for diseased predators and prey at the disease-free equilibrium point. Optimal treatment options for vulnerable and infected populations are established by applying optimal control theory to the ecoepidemiology model of a prey-predator system. MATLAB software is utilized to obtain numerical simulations that validate the analytical outcomes. The optimal control problem simulations demonstrate that the number of infected populations in a given prey-predator system can be decreased by implementing control measures.

A predator-prey fractional model with disease in the prey species.

In this paper, we study a generalized eco-epidemiological model of fractional order for the predator-prey type in the presence of an infectious disease in the prey. The proposed model considers that the disease infects the prey, causing them to be divided into two classes, susceptible prey and infected prey, with different density-dependent predation rates between the two classes. We propose logistic growth in both the prey and predator populations, and we also propose that the predators have alternative food sources (i.e., they do not feed exclusively on these prey). The model is evaluated from the perspective of the global and local generalized derivatives by using the generalized Caputo derivative and the generalized conformable derivative. The existence, uniqueness, non-negativity, and boundedness of the solutions of fractional order systems are demonstrated for the classical Caputo derivative. In addition, we study the stability of the equilibrium points of the model and the asymptotic behavior of its solution by using the Routh-Hurwitz stability criteria and the Matignon condition. Numerical simulations of the system are presented for both approaches (the classical Caputo derivative and the conformable Khalil derivative), and the results are compared with those obtained from the model with integro-differential equations. Finally, it is shown numerically that the introduction of a predator population in a susceptible-infectious system can help to control the spread of an infectious disease in the susceptible and infected prey population.

Analysis of stochastic disease including predator-prey model with fear factor and Lévy jump.

In this paper, we investigate the dynamical properties of a stochastic predator-prey model with a fear effect. We also introduce infectious disease factors into prey populations and distinguish prey populations into susceptible prey and infected prey populations. Then, we discuss the effect of Lévy noise on the population considering extreme environmental situations. First of all, we prove the existence of a unique global positive solution for this system. Second, we demonstrate the conditions for the extinction of three populations. Under the conditions that infectious diseases are effectively prevented, the conditions for the existence and extinction of susceptible prey populations and predator populations are explored. Third, the stochastic ultimate boundedness of system and the ergodic stationary distribution without Lévy noise are also demonstrated. Finally, we use numerical simulations to verify the conclusions obtained and summarize the work of the paper.

An advanced computing scheme for the numerical investigations of an infection-based fractional-order nonlinear prey-predator system.

The purpose of this study is to present the numerical investigations of an infection-based fractional-order nonlinear prey-predator system (FONPPS) using the stochastic procedures of the scaled conjugate gradient (SCG) along with the artificial neuron networks (ANNs), i.e., SCGNNs. The infection FONPPS is classified into three dynamics, susceptible density, infected prey, and predator population density. Three cases based on the fractional-order derivative have been numerically tested to solve the nonlinear infection-based disease. The data proportions are applied 75%, 10%, and 15% for training, validation, and testing to solve the infection FONPPS. The numerical representations are obtained through the stochastic SCGNNs to solve the infection FONPPS, and the Adams-Bashforth-Moulton scheme is implemented to compare the results. The infection FONPPS is numerically treated using the stochastic SCGNNs procedures to reduce the mean square error (MSE). To check the validity, consistency, exactness, competence, and capability of the proposed stochastic SCGNNs, the numerical performances using the error histograms (EHs), correlation, MSE, regression, and state transitions (STs) are also performed.

Solving an Infectious Disease Model considering Its Anatomical Variables with Stochastic Numerical Procedures.

The aim of the current work is to perform the numerical investigation of the infectious disease based on the nonlinear fractional order prey-predator model using the Levenberg–Marquardt backpropagation (LMB) based on the artificial neuron networks (ANNs), i.e., LMBNNs. The fractional prey-predator model is classified into three categories, the densities of the susceptible, infected prey, and predator populations. The statistics proportions for solving three different variations of the infectious disease based on the fractional prey-predator model are designated for training 80% and 10% for both validation and testing. The numerical actions are performed using the LMBNNs to solve the infectious disease based on the fractional prey-predator model, and comparison is performed using the database Adams–Bashforth–Moulton approach. The infectious disease based on the fractional prey-predator model is solved using the LMBNNs to reduce the mean square error (M.S.E). In order to validate the exactness, capability, consistency, and competence of the proposed LMBNNs, the numerical procedures using the correlation, M.S.E, regression, and error histograms are drawn.

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

The fear response is an important anti-predator adaptation that can significantly reduce prey's reproduction by inducing many physiological and psychological changes in the prey. Recent studies in behavioral sciences reveal this fact. Other than terrestrial vertebrates, aquatic vertebrates also exhibit fear responses. Many mathematical studies have been done on the mass mortality of pelican birds in the Salton Sea in Southern California and New Mexico in recent years. Still, no one has investigated the scenario incorporating the fear effect. This work investigates how the mass mortality of pelican birds (predator) gets influenced by the fear response in tilapia fish (prey). For novelty, we investigate a modified fractional-order eco-epidemiological model by incorporating fear response in the prey population in the Caputo-fractional derivative sense. The fundamental mathematical requisites like existence, uniqueness, non-negativity and boundedness of the system's solutions are analyzed. Local and global asymptotic stability of the system at all the possible steady states are investigated. Routh-Hurwitz criterion is used to analyze the local stability of the endemic equilibrium. Fractional Lyapunov functions are constructed to determine the global asymptotic stability of the disease-free and endemic equilibrium. Finally, numerical simulations are conducted with the help of some biologically plausible parameter values to compare the theoretical findings. The order $\alpha$ of the fractional derivative is determined using Matignon's theorem, above which the system loses its stability via a Hopf bifurcation. It is observed that an increase in the fear coefficient above a threshold value destabilizes the system. The mortality rate of the infected prey population has a stabilization effect on the system dynamics that helps in the coexistence of all the populations. Moreover, it can be concluded that the fractional-order may help to control the coexistence of all the populations.

Effects of incubation and gestation periods in a prey–predator model with infection in prey

In this paper, we study a wide spectrum of dynamical features of a prey–predator model with infection in prey population only. In the model formulation, we consider nonlinear incidence for infection transmission and Holling type II as response function of predator. We analyze the model for local stability and Hopf bifurcation, and the theoretical results are validated and extrapolated by numerical simulations. Also, we perform sensitivity analysis to explore the significance of the crucial parameters influencing the densities of prey and predator populations. Our numerical results show that disease persists in the system even if the basic reproduction number is below unity. The rates of predation on susceptible and infected prey populations are shown to dramatically change the behavior of eco-epidemiological system. We extend our model by considering the fact that the newly infected prey becomes productively infectious after the effective contact between susceptible and infectious preys, and some time lag is involved in this biological process; also the conversion process conceals some time. We analyze our eco-epidemiological model with two time delays (incubation delay and predator’s gestation delay) for stability and bifurcation. From numerical simulations, we observe that both the delay parameters substantially affect the stable configuration of the system.

Dynamics of a fractional epidemiological model with disease infection in both the populations

In order to depict a situation of possible spread of infection from prey to predator, a fractional-order model is developed and its dynamics is surveyed in terms of boundedness, uniqueness, and existence of the solutions. We introduce several threshold parameters to analyze various points of equilibrium of the projected model, and in terms of these threshold parameters, we have derived some conditions for the stability of these equilibrium points. Global stability of axial, predator-extinct, and disease-free equilibrium points are investigated. Novelty of this model is that fractional derivative is incorporated in a system where susceptible predators get the infection from preys while predating as well as from infected predators and both infected preys and predators do not reproduce. The occurrences of transcritical bifurcation for the proposed model are investigated. By finding the basic reproduction number, we have investigated whether the disease will become prevalent in the environment. We have shown that the predation of more number of diseased preys allows us to eliminate the disease from the environment, otherwise the disease would have remained endemic within the prey population. We notice that the fractional-order derivative has a balancing impact and it assists in administering the co-existence among susceptible prey, infected prey, susceptible predator, and infected predator populations. Numerical computations are conducted to strengthen the theoretical findings.

Bioeconomic-Epidemiological Model of Scomber colias Population in the Moroccan Coasts

In this paper, we develop and study a mathematical model for the dynamics of Scomber colias and Thunnus thynnus prey-predator with parasitic helminths. We search to analyze a bioeconomic model in which both susceptible and infected prey populations Scomber colias are exposed to the predator Thunnus thynnus, with varying degrees of exposure. However, the predator feeds preferentially on the most numerous prey types. This implies a kind of switching from the susceptible class to the infected class, and vice versa, as these two types of prey change in numerical superiority. So, the positivity, boundedness, equilibria, stability, and bioeconomic equilibrium are studied. Some numerical simulation of stability is cited. For giving a high yield and keeping the Scomber colias and Thunnus thynnus populations away from extension, we use the Maximum Principle of Pontryagin.

Stability and bifurcation analysis of a diffusive modified Leslie-Gower prey-predator model with prey infection and Beddington DeAngelis functional response

In this paper, we present and analyze a spatio-temporal eco-epidemiological model of a prey predator system where prey population is infected with a disease. The prey population is divided into two categories, susceptible and infected. The susceptible prey is assumed to grow logistically in the absence of disease and predation. The predator population follows the modified Leslie-Gower dynamics and predates both the susceptible and infected prey population with Beddington-DeAngelis and Holling type II functional responses, respectively. The boundedness of solutions, existence and stability conditions of the biologically feasible equilibrium points of the system both in the absence and presence of diffusion are discussed. It is found that the disease can be eradicated if the rate of transmission of the disease is less than the death rate of the infected prey. The system undergoes a transcritical and pitchfork bifurcation at the Disease Free Equilibrium Point when the prey infection rate crosses a certain threshold value. Hopf bifurcation analysis is also carried out in the absence of diffusion, which shows the existence of periodic solution of the system around the Disease Free Equilibrium Point and the Endemic Equilibrium Point when the ratio of the rate of intrinsic growth rate of predator to prey crosses a certain threshold value. The system remains locally asymptotically stable in the presence of diffusion around the disease free equilibrium point once it is locally asymptotically stable in the absence of diffusion. The Analytical results show that the effect of diffusion can be managed by appropriately choosing conditions on the parameters of the local interaction of the system. Numerical simulations are carried out to validate our analytical findings.

On the Dynamics of a Stochastic Ratio-Dependent Predator-Prey System with Infection for the Prey

In this paper, we investigate the dynamics of a stochastic predator-prey model with ratio-dependent functional response and disease in the prey. Firstly, we prove the existence and uniqueness of the positive solution for the stochastic model by using conventional methods. Then we obtain the threshold for the infected prey population, that is, the disease will tend to extinction if > 1. Finally, the sufficient condition on the existence of a unique ergodic stationary distribution is obtained, which indicates that all the populations are permanent in the time mean sense. Numerical simulations are conducted to verify our analysis results.

Interactive Effects of Disease Transmission on Predator-Prey Model

This paper deals with predator-prey eco-epidemiological model where an infectious disease among fish population is non-linearly transmitted in a reserve area. Then the disease is transmitted indirectly to the predator population during their feeding process. At the time of harvesting, both the susceptible and the infected prey population are harvested. When the nonlinear disease transmission and the inhibition effect on the dynamical behavior of the prey are measured, the number of infected individuals increases. The model in this study is analyzed in term of boundedness, and local and global stability under certain conditions and Hopf bifurcation. For the determine of optimal conditions, we have compared the theoretical results with numerical results for different sets of parameters.

DETERMINISTIC PREDATOR–PREY MODELS WITH DISEASE IN THE PREY POPULATION

A class of deterministic predator–prey systems, where the prey population is subject to an infectious disease, is studied. The disease can be transmitted both horizontally and vertically within the host population but cannot be spread between the two trophic levels. Using the mathematical tools of uniform persistence, we derive sufficient conditions for which the interacting populations can coexist. Criteria based on model parameters for which either only the infected prey or healthy prey persists are also provided. It is found through numerical investigations that predation can change competition outcomes between healthy and infected prey populations. Depending on the parameter regimes and initial conditions, predation can either eradicate or promote the disease. As infected prey provides a resource for the predators, disease may promote persistence of the predators. However, infected prey may dominate the predator–prey community if disease is very infectious. In addition, disease in the prey population can mediate a hydra effect in predators and may induce chaotic interactions.

Optimal control of a diffusive eco-epidemiological predator–prey model

In this study, we investigate the optimal control problem for a diffusion eco-epidemiological predator–prey model. We applied two controllers to this model. One is the separation control, which separates the uninfected prey from the infected prey population, and the other is used as a treatment control to decrease the mortality caused by the disease. Then, we propose an optimal problem to minimize the infected prey population at the final time and the cost cause by the controls. To do this, by the operator semigroup theory we prove the existence of the solution to the controlled system. Furthermore, we prove the existence of the optimal controls and obtain the first-order necessary optimality condition for the optimal controls. Finally, some numerical simulations are carried out to support the theoretical results.

Dynamical analysis of a fractional-order eco-epidemiological model with disease in prey population

A fractional-order eco-epidemiological model with disease in the prey population is formulated and analyzed. Mathematical analysis and numerical simulations are performed to clarify the characteristics of the proposed fractional-order model. The existence, uniqueness, non-negativity and boundedness of the solutions are proved. The local and global asymptotic stability of all equilibrium points are investigated. Finally, numerical simulations are conducted to illustrate the analytical results. The occurrence of Hopf bifurcations and transcritical bifurcations for the fractional-order eco-epidemiological model are demonstrated. It is observed that the fractional order has a stabilization effect and it may help to control the coexistence between susceptible prey, infected prey and predator populations.

Eco-epidemiological model with fatal disease in the prey

We investigate a model consisting of a predator population and both susceptible and infected prey populations. The predator can feed on either prey species but instead of choosing individuals at random the predator feeds preferentially on the most abundant prey species. More specifically we assume that the likelihood of a predator catching a susceptible prey or an infected prey is proportional to the numbers of these two different types of prey species. This phenomenon, involving changing preference from susceptible to infected prey, is called switching. Mukhopadhyay studied a switching model and proposed that the interaction of predators with infected prey is beneficial for the growth of the predator. In this model, we assume that the predator will eventually die as a result of eating infected prey. We find a threshold parameter R0 and showed that the disease will be eradicated from the system if R0<1.

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.