The stability of a predator-prey system with linear mass-action functional response perturbed by white noise.

Daqing Jiang,Xiangdan Wen,Zhenwen Liu,Qiumei Zhang

doi:10.1186/s13662-016-0776-8

Abstract

The present paper deals with the problem of an ecoepidemiological model with linear mass-action functional response perturbed by white noise. The essential mathematical features are analyzed with the help of the stochastic stability, its long time behavior around the equilibrium of deterministic ecoepidemiological model, and the stochastic asymptotic stability by Lyapunov analysis methods. Numerical simulations for a hypothetical set of parameter values are presented to illustrate the analytical findings.

Highlights

In an ecosystem, species does not exist alone while it spreads the disease: it competes with the other species for space or food or is predated by other species
It is essential to consider the effect of interacting species when we study the dynamical behaviors of epidemiological models
On the basis of this model, the authors in [ ] studied and compared the dynamics of the proposed ecoepidemiological model to explore the crucial system parameters and their ranges in order to obtain different theoretical behaviors predicted from the interactions between susceptible prey, infected prey, and their predators

Summary

Introduction

Species does not exist alone while it spreads the disease: it competes with the other species for space or food or is predated by other species. Zhang et al Advances in Difference Equations (2016) 2016:54 the death rate of pelicans and is considered to contribute negative growth, whereas feeding on susceptible fish enhances their growth rate and is considered to contribute positive growth In their model they did not consider that the portion of infected fish recovered and became susceptible. On the basis of this model, the authors in [ ] studied and compared the dynamics of the proposed ecoepidemiological model to explore the crucial system parameters and their ranges in order to obtain different theoretical behaviors predicted from the interactions between susceptible prey, infected prey, and their predators. ⎪⎩ddPI((tt))==((λ–Sθ(βt)II((tt))P–(tβ) –I(tδ)PP((tt))+–θμαIS(t()t))Pdt(t+))σdSt.(t)I(t) dB(t), In this paper, we study the dynamics of the ecoepidemiological model with linear massaction functional response perturbed by white noise to explore the crucial system parameters and their ranges in order to obtain different theoretical behaviors predicted from the interactions between susceptible prey, infected prey, and their predators.

I – I – I log

Conclusion