一类具有资源约束的SIS流行病模型的随机动力学

Stochastic dynamics of an SIS epidemic model with resource constraints

为研究环境随机性对流行病传播动态的影响,利用随机微分方程组构建了一类具有资源约束的随机易感者-感染者-易感者(SIS)流行病动力学模型.首先,通过构造Lyapunov函数,证明了随机流行病模型全局正解的存在性和唯一性;其次,采用数值模拟仿真分析了流行病在不同场景下的灭绝概率和灭绝时间.研究结果表明,环境随机性的强度与流行病的灭绝概率呈正相关关系,与流行病的灭绝时间呈负相关关系.特别地,当感染者规模接近吸引盆地的边界时,流行病更容易发生灭绝.该理论框架可拓展到其他流行病模型的研究中.

To investigate the influence of environmental stochasticity on the dynamics of epidemic spread,a stochastic susceptible-infectious-susceptible(SIS)epidemiological model with resource constraints is constructed by using stochastic differential equations.Firstly,the existence and uniqueness ofthe global positive solutions of the stochastic epidemic model are proven by constructing Lyapunov function.Utilizing numerical simulation methods,the probability and duration of epidemic extinction are analyzed under various scenarios.The results show that the intensity of environmental stochasticity ispositively correlated with the extinction probability of epidemic,and negatively correlated with the extinction time of epidemic.Specifically,when thescale of infectives approaches the boundary of an attractor basin,epidemic extinction is more likely to occur.The theoretical framework proposed inthis study can be extended to the study of other epidemic models.