Fan Kuangang, Zhang Yan, Gao Shujing, Chen Shihua
School of Mechanical and Electrical Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, PR China.
College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, PR China.
Physica A. 2020 Apr 15;544:123379. doi: 10.1016/j.physa.2019.123379. Epub 2019 Nov 4.
A stochastic susceptible-infectious-recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity, vaccination, and Le.´vy jumps on the transmission of diseases. We first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system. Sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable Lyapunov functions. Based on the analysis, we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system.
建立了一个具有非线性发病率的随机易感-感染-康复流行病模型，以讨论暂时免疫、疫苗接种和 Lévy 跳跃对疾病传播的影响。我们首先确定了该随机系统唯一全局正解的存在性以及一个正不变集。然后，通过构造合适的 Lyapunov 函数，得到了疾病灭绝和均值持续存在的充分条件。基于分析，我们得出噪声强度和疫苗接种有效期对系统的传播动力学有很大影响的结论。
