Stability analysis of SAIR mathematical model with general incidence rates and temporary immunity

This paper studies the dynamics of a SAIR mathematical model that describes the interaction among susceptible, asymptomatic, symptomatic, and recovered individuals. Two general incidence functions describing the infection caused by the asymptomatic and symptomatic individuals are introduced. We also take into account a temporary immunity, that is, a proportion of the recovered individuals becomes susceptible again. The basic reproduction number R_۰ depends on the general incidence functions. The local and global asymptotical stability for each equilibrium will depend on the basic reproduction number R_۰. In precise terms, the disease-free equilibrium is locally and globally asymptotically stable when R_۰<۱, while   the endemic equilibrium is locally and globally asymptotic stable when R_۰>۱. The numerical simulation is performed for different incidence rate cases, such as bilinear, Beddington-DeAngelis, Crowley Martin, and non-monotonic incidence rate functions. The simulation results are found to agree with the theoretical endings.

کلیدواژه ها:

SAIR mathematical model ، Stability ، Basic reproduction number ، Periodic orbit