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Bulletin of Mathematical Biology

, Volume 71, Issue 1, pp 75–83 | Cite as

Global Properties of SIR and SEIR Epidemic Models with Multiple Parallel Infectious Stages

  • Andrei Korobeinikov
Original Article

Abstract

We consider global properties of compartment SIR and SEIR models of infectious diseases, where there are several parallel infective stages. For instance, such a situation may arise if a fraction of the infected are detected and treated, while the rest of the infected remains undetected and untreated. We assume that the horizontal transmission is governed by the standard bilinear incidence rate. The direct Lyapunov method enables us to prove that the considered models are globally stable: There is always a globally asymptotically stable equilibrium state. Depending on the value of the basic reproduction number R 0, this state can be either endemic (R 0>1), or infection-free (R 0≤1).

Keywords

Infectious disease Mass-action Endemic equilibrium state Global stability Direct Lyapunov method Lyapunov function 

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Copyright information

© Society for Mathematical Biology 2008

Authors and Affiliations

  1. 1.MACSI, Department of Mathematics and StatisticsUniversity of LimerickLimerickIreland

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