Abstract

Stochastic epidemic models with varying infectivity and waning immunity have been recently introduced. Those models are more realistic than classical SIRS -type models, but also more difficult to study from a mathematical point of view since the underlying process is no more a Markov process. I will present results obtained by Forien et al. (2022) on the equilibrium of such a models, and by Foutel-Rodier et al. (2023) when a vaccination policy is taken into account. I also will focus on a new model, introduced in collaboration with  Arsène Brice Zotsa-Ngoufack, using the same framework, but with memory of past infections: at each new infection, the new infectivity and susceptibility depend on their previous values. The main questions related to such models are the long time behavior of the epidemic, and the existence of an endemic equilibrium.