A Geometric Analysis of the SIRS Model with Secondary Infections
Panagiotis Kaklamanos, Andrea Pugliese, Mattia Sensi, Sara Sottile
Source abstract
Abstract. We propose a compartmental model for a disease with temporary immunity and secondary infections. From our assumptions on the parameters involved in the model, the system naturally evolves in three time scales. We characterize the equilibria of the system and analyze their stability. We find conditions for the existence of two endemic equilibria for some cases in which [Formula: see text]. Then, we unravel the interplay of the three time scales, providing conditions to foresee whether the system evolves in all three scales, or only in the fast and the intermediate ones. We conclude with numerical simulations and bifurcation analysis to complement our analytical results.
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