TITLE:
Dynamic Analysis for a SIQR Epidemic Model with Specific Nonlinear Incidence Rate
AUTHORS:
Jie Xu, Tiansi Zhang
KEYWORDS:
Epidemic Model, Specific Nonlinear Incidence Rate, Lyapunov Function, Stability, Existence, Persistence
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.7 No.8,
August
23,
2019
ABSTRACT: The article investigates a SIQR epidemic model with specific nonlinear incidence rate and stochastic model based on the former, respectively. For deterministic model, we study the existence and stability of the equilibrium points by controlling threshold parameter R0 which determines whether the disease disappears or prevails. Then by using Routh-Hurwitz criteria and constructing suitable Lyapunov function, we get that the disease-free equilibrium is globally asymptotically stable if R0 or unstable if R0>1. In addition, the endemic equilibrium point is globally asymptotically stable in certain region when R0>1. For the corresponding stochastic model, the existence and uniqueness of the global positive solution are discussed and some sufficient conditions for the extinction of the disease and the persistence in the mean are established by defining its related stochastic threshold R0s. Moreover, our analytical results show that the introduction of random fluctuations can suppress disease outbreak. And numerical simulations are used to confirm the theoretical results.