2017/07/20 by Dan Li, Shengqiang Liu, Jing'an Cui +1
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #Applied mathematics #Basic reproduction number #COVID-19 epidemiological studies #Convergence (economics) #Ergodic theory #Ergodicity #Evolution and Genetic Dynamics #Limit (mathematics) #Markov chain #Markov process #Mathematical analysis #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Measure (data warehouse) #Population #Pure mathematics #Statistical physics #Statistics #math.DS #msc:60H10 #msc:92D25 #msc:92D30 #msc:93E15
paper · pdf · doi:10.1016/j.jde.2017.08.066
published as Journal of Differential Equations: 263(2017): 8873--8915
arxiv created 2017/07/20 · openalex publication_date 2017/09/13 · arxiv updated 2017/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
This paper studies the spread dynamics of a stochastic SIRS epidemic model with nonlinear incidence and varying population size, which is formulated as a piecewise deterministic Markov process. A threshold dynamic determined by the basic reproduction number R0 is established: the disease can be eradicated almost surely if R0<1, while the disease persists almost surely if R0>1. The existing method for analyzing ergodic behavior of population systems has been generalized. The modified method weakens the required conditions and has no limitations for both the number of environmental regimes and the dimension of the considered system. When R0>1, the existence of a stationary probability measure is obtained. Furthermore, with the modified method, the global attractivity of the Ω-limit set of the system and the convergence in total variation to the stationary measure are both demonstrated under a mild extra condition.