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Section B

Effect of cross-immunity on the transmission dynamics of two strains of dengue

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Pages 2361-2384 | Received 11 Sep 2008, Accepted 05 Nov 2008, Published online: 25 May 2010
 

Abstract

A deterministic model for the transmission dynamics of two strains of dengue disease is presented. The model, consisting of mutually exclusive epidemiological compartments representing the human and vector dynamics, has a locally asymptotically stable, disease-free equilibrium whenever the maximum of the associated reproduction numbers of the two strains is less than unity. The model can have infinitely many co-existence equilibria if infection with one strain confers complete cross-immunity against the other strain and the associated reproduction number of each strain exceeds unity. On the other hand, if infection with one strain confers partial immunity against the other strain, disease elimination, competitive exclusion or co-existence of the two strains can occur. The effect of seasonality on dengue transmission dynamics is explored using numerical simulations, where it is shown that the oscillation pattern differs between the strains, depending on the degree of the cross-immunity between the strains.

2000 AMS Subject Classifications :

Additional information

Notes on contributors

S. M. Garba

Current address: Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa

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