Abstract
This work is devoted to investigate the existence and uniqueness of a global positive solution for a stochastic epidemic model with relapse and media coverage. We also study the dynamical properties of the solution around both disease-free and endemic equilibria points of the deterministic model. Furthermore, we show the existence of a stationary distribution. Numerical simulations are presented to confirm the theoretical results.
Highlights
Infectious disease is a major public health problem in the World
We investigate stochastic SIRI models, which consist of systems with three compartments: susceptibles, infectives, and removed, labeled by S, I and R
Li and Cui [20], Tchuenche et al [31], and Sun et al [30] used deterministic models to investigate the effects of media coverage on the transmission dynamics, by means of the following incidence function g(S, I) =
Summary
Infectious disease is a major public health problem in the World. Mathematical models have been widely used in providing quantitative predictions and evaluating interventions. Media coverage, Stochastic process, Stationary distribution, Ergodicity. Li and Cui [20], Tchuenche et al [31], and Sun et al [30] used deterministic models to investigate the effects of media coverage on the transmission dynamics, by means of the following incidence function g(S, I) =
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