Abstract
We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate. The stochastic model is derived from the deterministic epidemic model by introducing random perturbations around the endemic equilibrium state. The effect of random perturbations on the stability behavior of endemic equilibrium is discussed. Finally, numerical simulations are presented to illustrate our theoretical results.
Highlights
We investigate a stochastic SIR epidemic model with specific nonlinear incidence rate
Many mathematical models have been developed in order to understand disease transmissions and behavior of epidemics
One of the earliest of these models was used by Kermack and Mckendrick [1], by considering the total population into three classes, namely, susceptible (S) individuals, infected (I) individuals, and recovered (R) individuals which is known to us as SIR epidemic model
Summary
Many mathematical models have been developed in order to understand disease transmissions and behavior of epidemics. One of the earliest of these models was used by Kermack and Mckendrick [1], by considering the total population into three classes, namely, susceptible (S) individuals, infected (I) individuals, and recovered (R) individuals which is known to us as SIR epidemic model. This SIR epidemic model is very important in today’s analysis of diseases. Several authors proposed different forms of incidences rate in order to model this disease transmission process. We consider the following model with specific nonlinear incidence rate: dS = A − μS −. We present the stability analysis of our stochastic model (2).
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
