title: Global stability of an epidemic model with delay and general nonlinear incidence.
abstract: An SIR model with distributed delay and a general incidence function is studied. Conditions are given under which the system exhibits threshold behaviour: the disease-free equilibrium is globally asymptotically stable if R0 is less than 1 and globally attracting if R0=1; if R0 is larger than 1, then the unique endemic equilibrium is globally asymptotically stable. The global stability proofs use a Lyapunov functional and do not require uniform persistence to be shown a priori. It is shown that the given conditions are satisfied by several common forms of the incidence function.
authors.affiliation: Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada. ccmcc8@gmail.com
authors.forename: C Connell
authors.initials: CC
authors.lastname: McCluskey
mesh_terms: D050936:Basic Reproduction Number; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D004198:Disease Susceptibility / Q000453:epidemiology; D058872:Epidemics / Q000706:statistics & numerical data*; D006801:Humans; D015994:Incidence; D008954:Models, Biological; D017711:Nonlinear Dynamics