一类潜伏期传染且具有病毒变异的传染病模型  

An Infectious Disease Model with Virus Variation and Infectivity in the Incubation Period

作　　者：马怡婷 张太雷[1] 邓金超 刘俊利[2] MA Yiting;ZHANG Tailei;DENG Jinchao;LIU Junli(School of Science,Chang'an University,Xi'an 710064,China;School of Science,Xi'an Polytechnic University,Xi'an 710048,China)

机构地区：[1]长安大学理学院,陕西西安710064 [2]西安工程大学理学院,陕西西安710048

出　　处：《山西大学学报（自然科学版）》2023年第3期574-584,共11页Journal of Shanxi University(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划(2022JM-023,2021JM-445)。

摘　　要：针对COVID-19的特点,建立了一类潜伏期与染病期均传染且具有病毒变异的SEI1I2QR传染病模型。首先,得到了模型的基本再生数与平衡点,利用Routh-Hurwitz判据、Lyapunov函数及LaSalle不变集原理证明了各类平衡点的全局稳定性。其次,选取印度的COVID-19累计病例数,对模型的参数进行了估计,并对疫情发展趋势进行了数值模拟。最后,对部分参数进行了敏感性分析,结果表明,易感者与潜伏者的有效接触率、易感者与病毒变异前的染病者的有效接触率和基本再生数之间存在强相关性关系,降低易感者与染病者的有效接触率可以有效控制疫情的进一步蔓延。According to the characteristics of COVID-19,an SEI1 I2QR infectious disease model with virus variation and infection in both incubation and infection period was established in this paper.Firstly,the basic reproduction number and the equilibrium point of the model was obtained,and the global stability of various equilibrium was proved by using Routh-Hurwitz criterion,Lyapunov function and LaSalle invariant set principle.Secondly,the cumulative number of COVID-19 cases in India was chosen to estimate the parameters of the model and simulate the trend of disease development.Finally,the sensitivity analysis was carried out on some parameters.The results show that the parameters with most influence on the basic reproduction number are the effective contact rate between susceptible individual and latent people,the effective contact rate between susceptible individual and infected individual before virus mutation.Reducing the effective contact rate between susceptible individuals and infected individuals can effectively control the further spread of the disease.

关 键 词：传染病模型建模 潜伏期 病毒变异 全局稳定性 

分 类 号：O175[理学—数学]