一类具有连续接种和潜伏期的流行病模型的稳定性分析

Stability analysis of a class of epidemic models with continuous inoculation and incubation periods

研究了一类具有连续接种免疫和潜伏期的SEIVR流行病模型,通过计算下一代矩阵得到了疾病流行与否的阈值-基本再生数.并运用Routh-Hurtwiz判据,Lyapunov函数以及La Salle不变集原理证明了当R0<1时,模型存在唯一的无病平衡点P0,且P0全局渐近稳定;当R0>1时,模型存在两个平衡点,无病平衡点P0不稳定,地方病平衡点P*全局渐近稳定.进一步分析得到在疾病防控中可以通过增加疫苗接种比率θ来降低基本再生数R0,从而防止疾病蔓延,并进行数值模拟验证了理论结果的正确性.

In this paper,a SEIVR epidemic model with continuous vaccination immunity and incubation period wasstudied.By calculating the next generation matrix,the threshol -the number of basic regeneration-R0 was obtained.Using Routh-Hurtwiz criterion,Lyapunov function and LaSalle invariant set principle,it was proved that when R0〈1,the model has a unique disease -free equilibrium point and the disease -free equilibrium point is globallyasymptotically stable.When R0〉1,the model has two equilibrium points,the disease-free equilibrium point is unstable,and the local disease -free equilibrium point is globally asymptotically stable.Further analysis can get in diseasecontrol and prevention by increasing the ratio of vaccination θ to reduce the basic reproductive number,so as toprevent the spread of disease.And at the end of the article for the correctness of the numerical simulation to verifythe the oretical results.