TY - JOUR
T1 - A stochastic epidemic model incorporating media coverage
AU - Cai, Yongli
AU - Kang, Yun
AU - Banerjee, Malay
AU - Wang, Weiming
N1 - Funding Information:
Supported in part by Simons Collaboration Grants for Mathematicians (208902) and the research scholarship from School of Letters and Sciences. Supported in part by the National Science Foundation of China (61373005) and Zhejiang Provincial Natural Science Foundation (LY12A01014).
PY - 2016
Y1 - 2016
N2 - 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.
AB - 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.
KW - Epidemic model
KW - Ergodic property
KW - Lyapunov function
KW - Stochastic asymptotic stability
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U2 - 10.4310/CMS.2016.v14.n4.a1
DO - 10.4310/CMS.2016.v14.n4.a1
M3 - Article
AN - SCOPUS:84963745317
SN - 1539-6746
VL - 14
SP - 893
EP - 910
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 4
ER -