title: The global stability of an SIRS model with infection age.
abstract: Infection age is an important factor affecting the transmission of infectious diseases. In this paper, we consider an SIRS model with infection age, which is described by a mixed system of ordinary differential equations and partial differential equations. The expression of the basic reproduction number R0 is obtained. If R0≤1 then the model only has the disease-free equilibrium, while if R0>1 then besides the disease-free equilibrium the model also has an endemic equilibrium. Moreover, if R0<1 then the disease-free equilibrium is globally asymptotically stable otherwise it is unstable; if R0>1 then the endemic equilibrium is globally asymptotically stable under additional conditions. The local stability is established through linearization. The global stability of the disease-free equilibrium is shown by applying the fluctuation lemma and that of the endemic equilibrium is proved by employing Lyapunov functionals. The theoretical results are illustrated with numerical simulations.
authors: Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, Shanxi, China. ychen@wlu.ca.
authors: Yuming
authors: Y
authors: Chen
authors: Junyuan
authors: J
authors: Yang
authors: Fengqin
authors: F
authors: Zhang
mesh_terms: D050936:Basic Reproduction Number / Q000706:statistics & numerical data; D019295:Computational Biology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D007239:Infections / Q000453:epidemiology* / Q000635:transmission*; D055641:Mathematical Concepts; D008954:Models, Biological; D015233:Models, Statistical; D013997:Time Factors