title: Global properties of infectious disease models with nonlinear incidence.
abstract: We consider global properties for the classical SIR, SIRS and SEIR models of infectious diseases, including the models with the vertical transmission, assuming that the horizontal transmission is governed by an unspecified function f(S,I). We construct Lyapunov functions which enable us to find biologically realistic conditions sufficient to ensure existence and uniqueness of a globally asymptotically stable equilibrium state. This state can be either endemic, or infection-free, depending on the value of the basic reproduction number.
authors: Laboratory of Nonlinear Science and Computation, Research Institute for Electronic Science, Hokkaido University, Sapporo, 060-0812, Japan. andrei@nsc.es.hokudai.ac.jp
authors: Andrei
authors: A
authors: Korobeinikov
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D018562:Disease Transmission, Infectious; D004812:Epidemiologic Methods; D005260:Female; D006801:Humans; D007231:Infant, Newborn; D018445:Infectious Disease Transmission, Vertical; D008297:Male; D008433:Mathematics; D008954:Models, Biological; D017711:Nonlinear Dynamics; D011156:Population Density; D011247:Pregnancy