title: Global dynamics of a staged-progression model with amelioration for infectious diseases.
abstract: We analyze the global dynamics of a mathematical model for infectious diseases that progress through distinct stages within infected hosts with possibility of amelioration. An example of such diseases is HIV/AIDS that progresses through several stages with varying degrees of infectivity; amelioration can result from a host's immune action or more commonly from antiretroviral therapies, such as highly active antiretroviral therapy. For a general n-stage model with constant recruitment and bilinear incidence that incorporates amelioration, we prove that the global dynamics are completely determined by the basic reproduction number R(0). If R(0)≤1, then the disease-free equilibrium P(0) is globally asymptotically stable, and the disease always dies out. If R(0)>1, P(0) is unstable, a unique endemic equilibrium P* is globally asymptotically stable, and the disease persists at the endemic equilibrium. Impacts of amelioration on the basic reproduction number are also investigated.
authors.affiliation: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada, T6G 2G1.
authors.forename: Hongbin
authors.initials: H
authors.lastname: Guo
authors.forename: Michael Y
authors.initials: MY
authors.lastname: Li
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology*; D018450:Disease Progression; D014943:Global Health; D006801:Humans; D015233:Models, Statistical