The Anderson Model And Siqs Of Model-based Infectious Disease Dynamics Research

In this paper we first consider the dynamical Anderson model of infectious disease, which is a extensive and representative cubic system. The analytical method is similar to the common SIR model and fourth order system. The global existence and uniqueness of the nonnegative solution are obtained by using Lipschitz condition and Picard theorem. Moreover, the stability of zero solution and the global stability of nontrivial solution in special condition are discussed by using the Lyapunov theorem.Next, a SIQS epidemic model, incorporates constant recruitment and a general population size dependent contact rate, is proposed .A threshold parameterσis identified. It is shown that, the disease-free equilibrium is globally stable whenσ≤1, and a unique endemic equilibrium is locally asymptotically stable asσ> 1. For the SIQS model with the quarantine-adiusted incidence, global stability of the endemic equilibrium is also proved.