ABSTRACT

Stochastic noise can affect the dynamics of infectious diseases. In this paper, a new stochastic multi-strain epidemic model with white noise, Markovian switching, vaccination control and age structure is established. Some priori estimates of the susceptible, infected and recovered are obtained. Under the condition of the objective function is minimised, we formulate sufficient and necessary conditions for the near-optimal control problems of the system, which is using a nearly maximum condition of the Hamiltonian function. The great influence of age structure, white noise, Markovian switching and vaccination control on the dynamical behaviour of infectious diseases and the existence of near-optimal control are demonstrated by numerical simulations.

摘要

随机噪声会影响传染病的动态。本文建立了一种新的具有白噪声、马尔可夫切换、疫苗接种控制和年龄结构的随机多株流行病模型。获得了易感者、感染者和康复者的一些先验估计。在目标函数最小化的条件下，我们为系统的近似最优控制问题制定了充分必要条件，即使用哈密顿函数的近似最大条件。数值模拟证明了年龄结构、白噪声、马尔可夫切换和疫苗接种控制对传染病动力学行为的巨大影响以及接近最优控制的存在。