In epidemiology, the search for new behaviour of infectious agents, processes and mechanisms of diffusion of infection of emerging infectious diseases caused by global warming has already led to tangible results. This paper proposes a dynamic endemic model Susceptible, Exposed, Precontaged, Infected, Retired, Susceptible (SEPIRS). This model is specialized in epidemics that persist for a long time and in cases where the infection spreads directly: first between pre-contagious individuals (asymptomatic) and susceptible individuals, second between infectious individuals (symptomatic) and susceptible individuals. This model characterises the individual recovering from an infection to develop a temporary immunity and then become susceptible again after some time.
                        
                        
                        
                        
                            
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