In this paper, we study the global properties of an SIR epidemic
model with distributed delays, where there are several parallel
infective stages, and some of the infected cells are detected and
treated, which others remain undetected and untreated. The model
is analyzed by determining a basic reproduction number $R_0$, and
by using Lyapunov functionals, we prove that the infection-free
equilibrium $E^0$ of system (3) is globally
asymptotically attractive when $R_0\leq 1$, and that the unique
infected equilibrium $E^*$ of system (3) exists and it is
globally asymptotically attractive when $R_0>1$.
Citation: Xia Wang, Shengqiang Liu. Global properties of a delayed SIR epidemicmodel with multiple parallel infectious stages[J]. Mathematical Biosciences and Engineering, 2012, 9(3): 685-695. doi: 10.3934/mbe.2012.9.685
Abstract
In this paper, we study the global properties of an SIR epidemic
model with distributed delays, where there are several parallel
infective stages, and some of the infected cells are detected and
treated, which others remain undetected and untreated. The model
is analyzed by determining a basic reproduction number $R_0$, and
by using Lyapunov functionals, we prove that the infection-free
equilibrium $E^0$ of system (3) is globally
asymptotically attractive when $R_0\leq 1$, and that the unique
infected equilibrium $E^*$ of system (3) exists and it is
globally asymptotically attractive when $R_0>1$.