We derive and study a time-delayed SIR model with a general incidence rate. The time delay represents temporary immunity period, i.e. time from recovery to becoming susceptible again. Both trivial and endemic equilibria are found, and their stability is investigated. Using Lyapunov functional approach, the global stability of an endemic equilibrium is shown. Numerical simulations support our analytical conclusions and illustrate possible behaviour scenarios of the model. © 2004 Elsevier Ltd. All rights reserved.
Kyrychko, Y. N., & Blyuss, K. B. (2005). Global properties of a delayed SIR model with temporary immunity and nonlinear incidence rate. Nonlinear Analysis: Real World Applications, 6(3), 495–507. https://doi.org/10.1016/j.nonrwa.2004.10.001