Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence

C. Connell McCluskey

doi:10.3934/mbe.2010.7.837

Article Contents

2010, Volume 7, Issue 4: 837-850. Doi: 10.3934/mbe.2010.7.837

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Global stability of an $SIR$ epidemic model with delay and general nonlinear incidence

C. Connell McCluskey^1,

1.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario

Received: March 2010

Revised: July 2010

Published: September 2010

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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.

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Mathematics Subject Classification: Primary: 34K20, 92D30.

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