title: Dynamical behaviour of epidemiological models with sub-optimal immunity and nonlinear incidence.
abstract: In this paper we analyze the dynamics of two families of epidemiological models which correspond to transitions from the SIR (susceptible-infectious-resistant) to the SIS (susceptible-infectious-susceptible) frameworks. In these models we assume that the force of infection is a nonlinear function of density of infectious individuals, I. Conditions for the existence of backwards bifurcations, oscillations and Bogdanov-Takens points are given.
authors.affiliation: Instituto Gulbenkian de Ciência, Apartado 14, 2781-901 Oeiras, Portugal.
authors.forename: M G M
authors.initials: MG
authors.lastname: Gomes
authors.forename: A
authors.initials: A
authors.lastname: Margheri
authors.forename: G F
authors.initials: GF
authors.lastname: Medley
authors.forename: C
authors.initials: C
authors.lastname: Rebelo
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology / Q000276:immunology / Q000635:transmission; D004812:Epidemiologic Methods; D004813:Epidemiology / Q000706:statistics & numerical data*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D018448:Models, Immunological; D015233:Models, Statistical; D017711:Nonlinear Dynamics