Dynamics for an SIRS epidemic model with infection age and relapse on a scale-free network

A new SIRS epidemic model with infection age and relapse on a scale-free network is introduced. The basic reproduction number R-0 is defined. Asymptotic smoothness of solution and uniform persistence of system are proved. It is shown that the disease-free equilibrium is globally asymptotically stable by using Fluctuation Lemma if R-0 < 1 and the endemic equilibrium is globally asymptotically stable by constructing suitable Lyapunov functional if R-0 > 1. Effects of two immunization schemes are studied. Numerical simulations and sensitivity analysis are performed. Results manifest that infection age and degree of node play a significant role in controlling the emergence and spread of the epidemic disease. (C) 2019 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.