An Asymptotic Analysis of an Infection-Age-Dependent SIR Epidemic Model with Nonlinear Infectivity

The dynamical behavior of an infection-age-dependent SIR epidemic model with nonlinear infectivity is studied and the threshold, a basic reproductive number which determines the outcome of the infectious disease, is found. When the basic reproductive number is less than or equal to 1, there exists only the disease-free equilibrium. Moreover, when the basic reproductive number is less than 1, the disease-free equilibrium is globally asymptotically stable and the disease will die out, whereas, when the basic reproductive number is greater than 1, there exist both the disease-free equilibrium which is unstable and the endemic equilibrium which is locally asymptotically stable, and the disease will persist. The paper concludes with the relevant results of the corresponding ODE models.