Dynamic analysis of a stochastic eco‐epidemiological model with disease in predators

Abstract

It is widely accepted that epidemics in biological populations and stochasticity in the environments are two important components significantly influencing the real ecosystems. To more accurately reveal developmental changes of the population dynamics and explore effective control methods for infectious disease, in this paper, we first construct a stochastic ecoepidemiological model with disease in predators, and mathematically analyze the fundamental properties of the model. Then, we establish sufficient criterion for the existence of a unique ergodic stationary distribution of the positive solution. Also, we derive sufficient conditions, respectively, for three different extinction scenarios of populations: (i) The predators go extinct, only the prey persists; (ii) both the predators and prey go extinct; and (iii) the disease is eradicated from the system, both the predators and prey persist. Finally, we perform some numerical simulations under different interferences of environment to illustrate the main theoretical results.Especially, we observe that once the disease is eradicated from the system, then the predators and prey will coexist in an oscillatory manner. Our research indicates that the environmental noises have significant impacts on the

Global stability analysis and Hopf bifurcation due to memory delay in a novel memory‐based diffusion three‐species food chain system with weak Allee effect

“…The three-species food chain systems are common in nature, for example, algae-crustaceans-fishes is a classic food chain system, and it is of great practical significance to study the dynamic properties of food chain systems [1,2]. Food chain systems can transfer nutrients and energy through the interaction between populations, while maintaining the stability of the ecosystem.…”

A multi‐group SEIRI epidemic model with logistic population growth under discrete Markov switching: Extinction, persistence, and positive recurrence

“…Realistic mathematical models with noise effects have been developed in the last few years. [17][18][19][20][21] For instance, Din et al 18 developed a stochastic Markovian dynamics approach to describe the spreading of dengue and the threshold of the disease. Hussain et al 20 used a stochastic model to study the transmission dynamics of the novel coronavirus.…”

“…In real world, environmental noise inevitably affects the growth of organisms and the spread of diseases. Realistic mathematical models with noise effects have been developed in the last few years 17–21 . For instance, Din et al 18 developed a stochastic Markovian dynamics approach to describe the spreading of dengue and the threshold of the disease.…”

“…Hussain et al 20 used a stochastic model to study the transmission dynamics of the novel coronavirus. Zhang et al 21 constructed a stochastic eco‐epidemiological model with disease in predators, and analyzed the fundamental properties of their model. Furthermore, it has been shown that modeling the behavior of dynamical systems by stochastic differential equations with colored noises has more advantages than deterministic modeling 22–33 .…”

A brief discussion about a predator-prey model including disease in predators with the delay effect

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