一类具有年龄结构的溶瘤病毒模型的动力学行为分析

Global Dynamic Analysis of an Oncolytic Virus Model with Age Structure

本文考虑到溶瘤病毒感染肿瘤细胞的可能性取决于可以感染的肿瘤细胞的数量,引入了频率依赖性函数,建立了一类具有年龄结构的溶瘤病毒感染模型,并研究了模型的全局动力学行为.首先证明了模型解的存在唯一性,计算了基本再生数R_(0),得到了稳态的存在定理.之后通过分析特征方程特征根的分布,得到了稳态的局部稳定性结论.最后通过构造Lyapunov函数和运用LaSalle不变集原理,得到模型无感染稳态E^(0)和感染稳态E^(*)的全局稳定性结论:当R_(0)<1时,无感染稳态E^(0)是全局渐近稳定的;当R_(0)>1时,感染稳态E*是全局渐近稳定的.

In this paper,considering that the possibility of oncolytic virus infection of tumor cells depends on the number of tumor cells that can be infected,a frequency-dependent function is introduced to establish an age-structured oncolytic virus infection model,and the global dynamic behavior of the model is studied.Firstly,the existence and uniqueness of the solution of the model are proved,the basic reproduction number R_(0) is calculated,and the existence theorem of the steady state is obtained.Then,by analyzing the distribution of the characteristic roots of the characteristic equation,the local stability conclusion of the steady state is obtained.Finally,by constructing the Lyapunov function and using the LaSalle invariant set principle.The global stability theory of the infection-free steady state E^(0) and the infected steady state E^(*) are obtained:When R_(0)<1,the infection-free steady state E^(0) is globally asymptotically stable;when R_(0)>1,the infected steady state E*is globally asymptotically stable.