受媒体报道和治疗影响的传染病模型的最优控制分析

Optimal Control Analysis of Infectious Disease Model Affected by Media Coverage and Treatment

首先,建立了一个具有治疗措施和媒体报道的传染病模型,证明了无病平衡点的全局稳定性,分析了地方病平衡点的存在性及其局部稳定性,并给出了疾病的持久性.其次,为了减少感染者的数量并降低媒体报道和治疗过程中的经济成本,建立了传染病最优控制模型,利用最优控制理论分析了使经济成本最低且感染者人数最少的最优控制方法.最后,通过数值模拟分析了最优控制措施对疾病传播的影响.研究结果表明,对传染病只采取单一的控制措施是远远不够的,多种控制措施相结合才是抑制传染病流行的最佳策略.

Firstly,an infectious disease model with treatment measures and media reports is established,the global stability of the disease-free equilibrium is proved,the existence and local stability of the endemic equilibrium are analyzed,and the persistence of the disease is also given.Then,in order to reduce the number of infected persons and the economic costs in the process of media reports and treatment measures,the optimal control model of infectious diseases is established.The optimal control method to minimize the economic costs and the number of infected persons is analyzed by using the optimal control theory.Finally,the influence of the optimal control measures on the spread of diseases is analyzed by numerical simulations.It shows that it is far from enough to take a single control measure for infectious diseases,and the combination of multiple control measures is the best strategy to curb the prevalence of diseases.