Global stability of a delayed SIRS model with temporary immunity

This paper addresses a time-delayed SIRS model with a linear incidence rate. Immunity gained by experiencing the disease is temporary; whenever infected, the disease individuals will return to the susceptible class after a fixed period of time. First, the local and global stabilities of the infection-free equilibrium are analyzed, respectively. Second, the endemic equilibrium is formulated in terms of the incidence rate, and two sufficient conditions for its locally asymptotic stability are found, one being proved theoretically, while the other being shown by introducing an auxiliary optimization problem and solving this problem with the help of Matlab toolbox. Finally, by using a Lyapunov functional, a sufficient criterion for the global stability of the endemic equilibrium is established.