Asymptotic analysis of an SIQS epidemic model with varying total population size and quarantine measures

A class of SIQS epidemic model with vertical infection and varying total population size and quarantine measures was established, by employing the epidemic dynamic theory, and considering both the input and output of the population. The threshold conditions which guarantee the global asymptotic stable disease-free equilibrium and endemic equilibrium of the SIQS epidemic model are obtained using methods including Routh-Hurwitz bounded, Lyapunov function and generalized Bendixson-Dulac function. The results show that the spread and prevalence of a disease can be controlled within a certain range, and that quarantine measures can accelerate the extinction of the disease.