Periodic and Almost Periodic Solutions for a Non-Autonomous Respiratory Disease Model with a Lag Effect

This paper studies a kind of non-autonomous respiratory disease model with a lag effect. First of all, the permanence and extinction of the system are discussed by using the comparison principle and some differential inequality techniques. Second, it assumes that all coefficients of the system are periodic. The existence of positive periodic solutions of the system is proven, based on the continuation theorem in coincidence with the degree theory of Mawhin and Gaines. In the meantime, the global attractivity of positive periodic solutions of the system is obtained by constructing an appropriate Lyapunov functional and using the Razumikin theorem. In addition, the existence and uniform asymptotic stability of almost periodic solutions of the system are analyzed by assuming that all parameters in the model are almost periodic in time. Finally, the theoretical derivation is verified by a numerical simulation.