Asymptotic Properties and Stability Switch of a Delayed-Within-Host-Dengue Infection Model with Mitosis and Immune Response

Abstract

In this paper, a delayed-within-host-dengue infection model with mitosis and immune response is analyzed. The basic reproduction number is calculated and a detailed discussion on the local and global dynamics of the model is conducted. By using comparison arguments, it is shown that when 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, the existence of Hopf bifurcation and stability switch at the immunity-activated infection equilibrium of the model with or without delay is established. Furthermore, by means of Lyapunov functional and LaSalle’s invariance principle, sufficient conditions are obtained for the global stability of the immunity-activated infection equilibrium. Numerical simulations are given to illustrate the main theoretical results. The normal form is calculated to analyze some properties of the bifurcation periodic solution when the time delay is absent. Moreover, we carry out sensitivity analysis on basic reproduction number to determine crucial parameters that affect the stability of each of feasible equilibrium.