Modèle épidémiologique compartimental à délai pour le virus de la dengue
Dengue is a viral infection affecting from 100 to 400 million people each year. According to the WHO, "severe dengue is a leading cause of serious illness and death in some Asian and Latin American countries". This justifies the modelling of this illness's propagation in a population using mathematical compartmental models. Results of Forshey et al. on dengue fever seem to indicate the possibility that a dengue infection does not yield a long term immunity against the different dengue serotypes, and that an homotypical reinfection could be common. We study a SIRS model for the dengue virus that takes into account this loss of immunity via a system of delay differential equations. We characterize the stationary states and their stability in terms of the different parameters considered, in particular the basic reproduction ratios associated to each dengue serotype. We study the system's bifurcations in its main parameters, especially the Hopf bifurcations arising from the presence of a delay in the system of differential equations. Numerical simulations of the model are presented to represent the model's different regimes.
dengue compartmental models epidemiology delay differential equations retarded differential equations Hopf bifurcation