In this paper, we present a mathematical model to study the dynamics of a co-infection involving two diseases: one that confers tem- porary immunity and the other that confers permanent immunity, while incorporating the impact of information dissemination about temporary immunity disease. The study of the disease with temporary immunity shows the existence of a unique disease-free equilibrium E_0, which is stable when R_0 < 1 and when R_0 > 1 we prove the existence of an endemic equilibrum. The basic reproduction number of the co-infection model R_0^c is determined, and a sensitivity analysis of the parameters is conducted to highlight the most influential parameters. Optimal controls representing prevention efforts for both diseases have been performed.

Mathematical modeling, co-infection, stability, optimal control.