Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages - Xia Wang; Shengqiang Liu (Mathematical Biosciences and Engineering)
In this paper, we study the global properties of an SIR epidemicmodel with distributed delays, where there are several parallelinfective stages, and some of the infected cells are detected andtreated, which others remain undetected and untreated. The modelis analyzed by determining a basic reproduction number $R_0$, andby using Lyapunov functionals, we prove that the infection-freeequilibrium $E^0$ of system (3) is globallyasymptotically attractive when $R_0≤ 1$, and that the uniqueinfected equilibrium $E^*$ of system (3) exists and it isglobally asymptotically attractive when $R_0>1$.