Document Type

Article

Publication Date

10-2010

Department

Mathematics

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 < 1 and globally attracting if R0 = 1; if R0 > 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.

Comments

This article was originally published in Mathematical Biosciences and Engineering, 7(4): 837-850. (c) 2010 American Institute of Mathematical Sciences

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