Dynamical evolution of discrete epidemic models

The dynamical evolution of a deterministic epidemic model is studied. We model the system by taking into account an intermediate class of population, say infected, which after a latency period enter into the infectious class. A mortality rate induced by the disease is also considered. The system evolves towards a final state which may develop a catastrophic epidemic if small outbreaks of the disease emerge. The final size, the threshold and the severity of the epidemic are also analyzed and calculated for this model.