一类具有多时滞非局部扩散HIV潜伏感染模型的时空动力学分析

Spatio-temporal dynamics of HIV latent infection model with nonlocal dispersal and multiple intracellular delays

该文建立了一类具有多时滞非局部扩散HIV潜伏感染模型来研究HIV在宿主体内感染机制.具体地,考虑了初始病毒感染到HIV病毒成功整合到靶细胞DNA中和细胞感染到病毒产生这两个时滞,同时也考虑了空间异质环境中自由病毒的非局部扩散.首先证明了系统解半流的全局适定性,紧性和渐近光滑性,其次通过下一代再生算子定义给出基本再生数泛函表达式,以及其非局部算子扰动的特征值问题的主特征值与基本再生数的关系.利用无穷维系统的持久性理论研究了模型的一致持久性.再次,通过将本征函数设置为Lyapunov泛函的积分核讨论了系统全局阈值动力学.具体地,当R_(0)≤1时无感染平衡态是全局稳定的,否则系统感染平衡态是全局稳定的.最后通过数值模拟验证了理论结果.此外数值结果表明:(1)增加扩散率和减少细胞延迟时间将增加病毒的最终载量;(2)扩散内核函数影响R_(0)的值以及病毒的最终载量.这说明病毒非局部扩散和时滞在宿主内HIV感染过程中起着关键的作用.

In this paper,a nonlocal dispersal HIV latent infection model with multiple time delays is established to study the infection mechanism of HIV in the host.Specifically,the time delay between the initial virus infection and the successful integration of the HIV virus RNA into the target cell DNA,the time delay between neutralizing cell infection and the generation of the virus are both considered.At the same time,the non-local dispersal of the free virus in the space heterogeneous environment is also considered.Firstly,the global well-posedness,compactness and asymptotic smoothness of the solution semiflow of the system are proved.Secondly,the functional expression of the basic reproduction number is derived and the relationship between the principal eigenvalue and the basic reproduction number is proved,which is given by the definition of the next generation regeneration operator.The consistent persistence of the model is studied by using the persistence theory of infinite dimensional systems.Thirdly,the global threshold dynamics of the system is discussed by setting the eigenfunction as the integral kernel of the Lyapunov functional.Specifically,when R_(0)≤1,the infection-free steady state is globally stable,otherwise,the infection steady state is globally stable.Finally,the theoretical results are verified by numerical simulation.In addition,the numerical results show that:(1)increasing the dispersal rate and reducing the intracellular delays will increase thefinal viral load;(2)The dispersal kernel function influence the value of R_(0) and thefinal load of the virus.This shows that the nonlocal dispersal and intracellular delays play a key role in the process of HIV infection in the host.