Abstract

We introduce stochasticity into a multigroup SIR model with nonlinear incidence. We prove that when the intensity of white noise is small, the solution of stochastic system converges weakly to a singular measure (i.e., a distribution) ifℛ0≤1and there exists an invariant distribution which is ergodic ifℛ0>1. This is the same situation as the corresponding deterministic case. When the intensity of white noise is large, white noise controls this system. This means that the disease will extinct exponentially regardless of the magnitude ofℛ0.

Highlights

  • We introduce stochasticity into a multigroup SIR model with nonlinear incidence

  • Considering different contact patterns, distinct number of sexual partners, or different geography, and so forth, individual hosts are often divided into groups in modeling epidemic diseases

  • Multigroup models have been proposed in the literature to describe the transmission dynamics of infectious diseases in heterogeneous host populations

Read more

Summary

Introduction

Considering different contact patterns, distinct number of sexual partners, or different geography, and so forth, individual hosts are often divided into groups in modeling epidemic diseases. We will prove that when the intensity of white noise is small, the solution of system (3) converges weakly to a singular measure (i.e., a distribution) if R0 ≤ 1 and there exists an invariant distribution which is ergodic if R0 > 1. This is the same situation as in Proposition 1. Beretta et al [17] considered a stochastic SIR model with time delays and obtained asymptotic mean square stability conditions for positive equilibrium. X(t) ≡ 0 is a solution of (5), called the trivial solution or equilibrium position

Existence and Uniqueness of the Nonnegative Solution
Exponential Stability of Infectious Disease
Full Text
Published version (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