Lévy jump modelling with infinite activity for an epidemic model: effects of stochasticity on reinfection and relapse, with an optimization approach

Abstract

This study investigates a stochastic epidemic model with reinfection and relapse, incorporating Le´vy noise with infinite activity. We establish the existence and uniqueness of global positive solutions, and analyze extinction and persistence in the mean. An optimization approach is introduced to identify control strategies that minimize disease prevalence or promote eradication, based on a stochastic threshold. Numerical simulations support the theoretical results and highlight the effect of optimized interventions on disease dynamics.