具有时滞和体液免疫反应的宿主体内登革热感染模型的稳定性和Hopf分支

Stability and Hopf bifurcation of a with-in host dengue infection model with delay and humoral immune response

研究一类具有时滞和体液免疫反应的宿主体内登革热感染模型.通过分析特征方程,讨论了系统各可行平衡点的局部稳定性,得到了系统Hopf分支存在的充分条件.通过构造适当的Lyapunov函数并应用LaSalle不变性原理,证明了当基本再生数小于1时,未感染平衡点是全局渐近稳定的;当基本再生数大于1且无时滞时,得到了系统免疫激活感染平衡点全局渐近稳定的充分条件.最后,利用数值模拟验证了所得理论结果的可行性.

A with-in host dengue infection model with time delay and humoral immune response is studied. By analyzing the corresponding characteristic equation, the local stability of each of feasible equilibria of the model is investigated, and sufficient condition for the existence of Hopf bifurcation is obtained. By constructing appropriate Lyapunov function and applying LaSalle’s invariance principle,it is shown that if the basic reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable. When the basic reproduction number is greater than unity, sufficient condition is obtained for the global stability of the Immuno-activated infection equilibrium of the system without time delay. Finally, numerical simulations are carried out to illustrate the theoretical results.