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MODELING AND ANALYSIS OF HIV AND HEPATITIS C CO-INFECTIONS

D. P. MOUALEU

Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon

UMI 209 IRD/UPMC UMMISCO, Bondy, France

Project-Team GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon

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J. MBANG

Department of Mathematics, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon

UMI 209 IRD/UPMC UMMISCO, Bondy, France

Project-Team GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon

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R. NDOUNDAM

Department of Computer Sciences, Faculty of Science, University of Yaounde I, PO Box 812 Yaounde, Cameroon

UMI 209 IRD/UPMC UMMISCO, Bondy, France

Project-Team GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon

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S. BOWONG

Laboratory of Applied Mathematics, Department of Mathematics and Computer Science, Faculty of Science, University of Douala, PO Box 24157 Douala, Cameroon

UMI 209 IRD/UPMC UMMISCO, Bondy, France

Project-Team GRIMCAPE, LIRIMA, University of Yaounde I, Cameroon

Corresponding author.

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https://doi.org/10.1142/S0218339011004159Cited by:11 (Source: Crossref)

Abstract

Infection with the hepatitis C virus (HCV) is the most common coinfection in people with the human immunodeficiency virus (HIV), and hepatitis C is categorized as an HIV-related illness. The study of the joint dynamics of HIV and HCV present formidable mathematical challenges in spite the fact that they share similar routes of transmission. A deterministic model for the co-interaction of HCV and HIV in a community is presented and rigorously analyzed. The disease-free equilibrium is shown to be locally asymptotically stable when the associated epidemic threshold known as the basic reproduction number for the model is less than the unity. The Centre Manifold theory is used to show that the HCV only and HIV/AIDS only endemic equilibria are locally asymptotically stable when their associated reproduction numbers are greater than the unity. We compute two coexistence thresholds for the stability of boundary equilibria. Numerical results are presented to validate analytical results.

Keywords:

AMSC: 34A34, 34D23, 34D40, 92D30

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