基于lévy噪声的随机SIRS模型的拟最优控制  

The near optimal control problem of a stochastic SIRS model based on lévy noise

作　　者：戴晓娟[1] DAI Xiaojuan(School of Mathematics and Computer Science,Ningxia Normal University,Guyuan Ningxia 756099)

机构地区：[1]宁夏师范学院数学与计算机科学学院,宁夏固原756099

出　　处：《宁夏师范学院学报》2023年第4期35-46,共12页Journal of Ningxia Normal University

摘　　要：建立了一类基于lévy跳跃的不确定参数随机SIRS传染病模型.利用该模型研究了疫苗接种条件下的拟最优控制问题,使得治疗疾病过程中所花费的成本尽可能地小.根据伴随方程,给出了易感人群、感染人群和恢复人群的先验估计,并利用Hamiltonian函数和Gronwall不等式建立了拟最优控制的充分条件.In this paper,a stochastic SIRS infectious disease model with uncertain parameters based on lévy jump is established.This model is used to study the near optimal control problem under the condition of vaccination,which makes the cost of treating the disease as small as possible.According to the adjoint equation,priori estimates of susceptible population,infected population and recovered population are given,and sufficient conditions for near optimal control are established by using Hamiltonian function and Gronwall inequality.

关 键 词：SIRS传染病模型 不确定参数 lévy跳跃 疫苗接种 

分 类 号：O211.63[理学—概率论与数理统计]