The global dynamics for an age-structured SLIS model with the delay - Hongwu Tan; Xin Yang; Hui Cao (Boundary Value Problems, 2020)
Abstract This paper deals with the global dynamics for a SLIS epidemic model with infection age. In our model, we also consider the time delay in the progression from the latent individuals to becoming infectious individuals. We verify the well posedness of the model by changing it into an abstract nondensely defined Cauchy problem and find conditions for the existence of disease free equilibrium and endemic equilibrium. The theoretic analysis shows that the disease-free equilibrium is globally asymptotically stable as the basic reproduction number R 0 $R_{0}$ is less than unity and that the endemic equilibrium is locally asymptotically stable and the system is uniformly persistent as R 0 $R_{0}$ is greater than unity. The numerical simulations illustrate that the endemic equilibrium may be asymptotically stable as R 0 > 1 $R_{0}>1$ .