具有年龄结构和水平传播的媒介传染病模型研究

Analysis of vector-borne infectious disease model with age-structured and horizontal transmission

考虑到病毒变异和感染年龄的普遍存在性,提出了一类具有潜伏年龄和水平传播的媒介-宿主传染病模型,给出了基本再生数R_(0)的精确表达式,刻画了该模型无病平衡态和地方病平衡态的存在性.进一步,利用线性近似方法和构造合适的Lyapunov函数及LaSalle不变原理等方法,证明了当R_(0)<1时,无病平衡态E0是全局渐近稳定的,疾病也最终趋于灭绝;而当R_(0)>1时,地方病平衡态是全局渐近稳定的,疾病将持续下去而形成地方病.

Considering the prevalence of variations in virus strains and the age of infection,a vector-borne infectious disease model with latent age and horizontal transmission is proposed.An exact expression for the basic reproduction number,R_(0),is given,which characterizes the existence of the disease-free equilibrium and the endemic equilibrium for this model.Next,by using a combination of linear approximation methods,constructing suitable Lyapunov functions,LaSalle invariance principles,and other methods,we prove that if R_(0)<1,then the disease-free equilibrium has global asymptotic stability,and the disease will eventually become extinct;if R_(0)>1,then the endemic equilibrium is globally asymptotically stable,and the disease will continue to form an endemic disease.