A remark on a generic SEIRS model and application to cat retroviruses and fox rabies

We consider a SEIRS problem modelling the propagation of an epidemic disease through an unstructured animal population. Under fairly general assumptions concerning the vital dynamics and the incidence term, we give an explicit criterion for the stability of the largest disease-free stationary state. We apply our result to the Feline Immunodeficiency Virus and to the Feline Leukemia Virus, two retroviruses of domestic cats (Felis catus), and to the rabies virus for red foxes (Vulpes vulpes). Next, in the case of nonvertically transmitted diseases, we express the optimal proportion of vaccinated individuals as a generic function of the reproductive number when simple incidence terms are used.