Affiliation:
1. College of Mathematics and System Science, Xinjiang University, Urumqi 830046, China
Abstract
The paper mainly investigates a stochastic SIRS epidemic model with Logistic birth and nonlinear incidence. We obtain a new threshold value (R0m) through the Stratonovich stochastic differential equation, different from the usual basic reproduction number. If R0m<1, the disease-free equilibrium of the illness is globally asymptotically stable in probability one. If R0m>1, the disease is permanent in the mean with probability one and has an endemic stationary distribution. Numerical simulations are given to illustrate the theoretical results. Interestingly, we discovered that random fluctuations can suppress outbreaks and control the disease.
Funder
National Natural Science Foundation of China
Science and Technology Department of Xinjiang Uygur Autonomous Region
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
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