A stochastic epidemic model incorporating media coverage

Yongli Cai, Yun Kang, Malay Banerjee, Weiming Wang

Research output: Contribution to journalArticlepeer-review

74 Scopus citations

Abstract

In this paper, we investigate the effects of environment fluctuations on disease dynamics through studying the stochastic dynamics of an SIS model incorporating media coverage. The value of this study lies in two aspects: Mathematically, we show that the disease dynamics the SDE model can be governed by its related basic reproduction number RS0: if RS0 ≤1, the disease will die out stochastically, but if RS0 >1, the disease will break out with probability one. Epidemiologically, we partially provide the effects of the environment fluctuations affecting spread of the disease incorporating media coverage. First, noise can suppress the disease outbreak. Notice that RS0 <R0, and it is possible that RS0 <1<R0. This is the case when the deterministic model has an endemic while the SDE model has disease extinction with probability one. Second, two stationary distribution governed by RS0: If RS0 <1, it has disease-free distribution which means that the disease will die out with probability one; while RS0 >1, it has endemic stationary distribution, which leads to the stochastically persistence of the disease. In order to understand the role of media coverage on disease dynamics, we present some numerical simulations to validate the analytical findings. It is interesting to note that although some parameters have no role in determining Rs0 , however the strength of noise to the susceptible population and the parameters characterizing media affect play crucial role in determining the long term dynamics of the system.

Original languageEnglish (US)
Pages (from-to)893-910
Number of pages18
JournalCommunications in Mathematical Sciences
Volume14
Issue number4
DOIs
StatePublished - 2016

Keywords

  • Epidemic model
  • Ergodic property
  • Lyapunov function
  • Stochastic asymptotic stability

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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