modèle SIS

CONT: On considère une population close et on modélise la propagation d’une maladie infectieuse dans cette population. On suppose que les individus composant la population peuvent être dans l’un de deux états : ils sont susceptibles (à la maladie) s’ils n’ont pas contracté la maladie, et infectieux s’ils ont contracté la maladie et qu’ils la propagent. Cela définit donc deux compartiments, l’objet de la modélisation étant de décrire l’évolution du nombre d’individus dans chaque compartiment [...]
CONT: Ce modèle est appelé modèle SIS, pour susceptible-infectieux-susceptible.

CONT: The susceptible-infected-susceptible (SIS) model of Weiss and Dishon is one of the simplest models of endemic infections. The model describes the evolution of an infection in a fixed population, with no restriction on the possibility of reinfection of a previously infected and now recovered individual. This is in contrast to the venerable susceptible-infection-recovered (SIR) model, where reinfection is not permitted. Both models exhibit a threshold value of the infectivity, below which the infection immediately dies out. Below the threshold, where only a tiny fraction of the population is impacted, the two models have essentially equivalent statistical properties. Above the threshold, in the SIR model, the infection is self-limiting, since in a fixed population the number of potential new victims, the susceptible pool, is monotonically decreasing in size. The SIS model, on the other hand, describes an endemic infection which can (above the threshold) persist indefinitely, at least at the deterministic level. Thus, the statistics of infection size in the two models above the threshold are very different.