一类潜伏期具有传染性的流行病模型的稳定性

研究一类潜伏期和染病期均具有传染性和康复可能的SEIQ流行病模型,确定了疾病流行与否的阈,利用Routh-Hurwitz判据和LaSalle不变集原理得到无病平衡点的全局渐近稳定性,并借助广义Bendixson-Dulac定理得到地方病平衡点的全局渐近稳定性,最后将隔离率作为控制变量,用范数指标函数作为衡量控制变量的标准,得出该模型最优控制元的存在惟一性.

Stability and optimal control problems of epidemic model with infectivity in latent period

An SEIQ epidemic model with infectivity and recovery in both latent period and in-fected period was introduced .The basic reproduction number was established .By means of Routh-Hurwitz criterion and LaSalle invariant principle , the global stability of the disease-free equilibrium was proved .Using the generalized Bendixson -Dulac theorem , the global stability of the positive equilibrium was proved .The optimal control problems of the epidemic model by using the norm index function as the standard of the examining the control variable were discussed .