总人口规模变化的年龄结构MSEIR流行病模型的再生数

The Reproductive Number of Age-Structured MSEIR Epidemic Model with Varying Total Population Size

在总人口规模变化和疾病影响死亡率的假设下,讨论了带二次感染和接种疫苗的年龄结构MSEIR流行病模型.首先给出再生数R(ψ,λ)(这里ψ(a)是接种疫苗率,λ是总人口的增长指数)的显式表达式.其次,证明了当R(ψ,λ)<1时,系统的无病平衡态是稳定的;当R(ψ,λ)>1时,无病平衡态是不稳定的.

We discuss an age-structured MSEIR epidemic model with the loss of immunity and an age-dependent vaccination rate φ（a） under the assumption of varying total population size and death-rate dependent of some diseases. First, we obtain an explicit formula for the reproductive number R（φ,λ） where φ（a） is the vaccination rate and λ is the growth exponent of total population. Next, we prove that the dlsease-free steady state is linearly stable ifR（φ,λ） is less than one and unstable if R（φ,λ）is larger than one. Finally, we obtain formula for the critical reproductive numer under the assumption of constant-sized population as a special case.