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The threshold of a non‐autonomous SIRS epidemic model with stochastic perturbations
Author(s) -
Ji Chunyan,
Jiang Daqing
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4096
Subject(s) - mathematics , epidemic model , extinction (optical mineralogy) , statistical physics , biology , demography , physics , population , sociology , paleontology
In this paper, we investigate a stochastic non‐autonomous SIRS (susceptible‐infected‐recovered‐susceptible) model. The extinction and the prevalence of the disease are discussed, and so, the threshold is given. Especially, we show there is a positive nontrivial periodic solution. At last, some examples and simulations are provided to illustrate our results. Copyright © 2016 John Wiley & Sons, Ltd.