TY - JOUR
T1 - A stochastic SIRS epidemic model with infectious force under intervention strategies
AU - Cai, Yongli
AU - Kang, Yun
AU - Banerjee, Malay
AU - Wang, Weiming
N1 - Funding Information:
This research was supported by the National Science Foundation of China ( 61373005 ) and Zhejiang Provincial Natural Science Foundation , China ( LY12A01014 ). The research of Y. Kang was partially supported by NSF-DMS ( 1313312 ), Simons Collaboration Grants for Mathematicians ( 208902 ) and the research scholarship from College of Letters and Sciences.
Publisher Copyright:
© 2015 Elsevier Inc.
PY - 2015/12/15
Y1 - 2015/12/15
N2 - In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S<1, under mild extra conditions, the SDE system has a disease-free absorbing set which means the extinction of disease with probability one. If R0S>1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.
AB - In this paper, we extend a classical SIRS epidemic model with the infectious forces under intervention strategies from a deterministic framework to a stochastic differential equation (SDE) one through introducing random fluctuations. The value of our study lies in two aspects. Mathematically, by using the Markov semigroups theory, we prove that the reproduction number R0S can be used to govern the stochastic dynamics of SDE model. If R0S<1, under mild extra conditions, the SDE system has a disease-free absorbing set which means the extinction of disease with probability one. If R0S>1, under mild extra conditions, it has an endemic stationary distribution which leads to the stochastical persistence of the disease. Epidemiologically, we find that random fluctuations can suppress disease outbreak, which can provide us some useful control strategies to regulate disease dynamics.
KW - Epidemic model
KW - Markov semigroups
KW - Reproduction number
KW - Stationary distribution
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U2 - 10.1016/j.jde.2015.08.024
DO - 10.1016/j.jde.2015.08.024
M3 - Article
AN - SCOPUS:84943366139
SN - 0022-0396
VL - 259
SP - 7463
EP - 7502
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 12
ER -