Abstract
A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results.
Highlights
Mathematical models are used to study the interrelationship among species and their environment
The positive equilibrium solution plays a major role in changing the dynamical behavior
The study of dynamical behavior of the predator-prey model has been receiving more attention, and many efforts have been taken in the field of population dynamics by several authors
Summary
Mathematical models are used to study the interrelationship among species and their environment. We have used Holling type II response for both infected and susceptible prey interactions with the predator. This kind of functional response has been widely utilized as a part of biological systems, see few epidemic models [9,10,11] and chemostat model [12]. Many results that study stability, boundedness, and persistence have been presented for some ecological models with stochastic effect [6, 10, 15,16,17,18]. The predator-prey model with two species and ratio dependence is discussed to examine its stability of equilibrium solutions in [26].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
