Continuous and discrete approaches to the epidemiology of viral spreading in populations taking into account the delay of incubation time

A significant part of theoretical approaches to model viral spreading diseases in populations does not take into account the time delay between the contact with the viral particles and the transmitting state of the host. The question then becomes whether such a biological fact must become part of these models or not; thus imparing many theoretical reports. Also, ecological systems, as human agglomerates, are not spatialy homogeneous, and the ordinary differential equations to simulate these systems are subjected to assumptions which can be unrealistic, many times. Here we study the spreading of a viral contagious disease in a population of constant size using epidemiological models described in terms of delay differential equations and probabilistic cellular automata. The delay represents the characteristic time between a susceptible individual to acquire the virus and to become a transmitter of it. We conclude that such a delay does not affect the local stability of the equilibrium solutions in both approaches.