Analysis of vector-borne infectious disease model with age-structured and horizontal transmission
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摘要: 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
${\cal R}_0$ 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${\cal R}_0<1$ 时, 无病平衡态${\cal E}_{0}$ 是全局渐近稳定的, 疾病也最终趋于灭绝; 而当${\cal R}_0>1$ 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.Abstract: 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,${\cal 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${\cal R}_0 <1 $ , then the disease-free equilibrium has global asymptotic stability, and the disease will eventually become extinct; if${\cal R}_0>1$ , then the endemic equilibrium is globally asymptotically stable, and the disease will continue to form an endemic disease. -
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