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An epidemic model for the transmission dynamics of HIV and another pathogen

Published online by Cambridge University Press:  17 February 2009

S. M. Moghadas  and
A. B. Gumel
S. M. Moghadas
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada; e-mail: moghadas@cc.umanitoba.ca and gumelab@cc.umanitoba.ca.
A. B. Gumel
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada; e-mail: moghadas@cc.umanitoba.ca and gumelab@cc.umanitoba.ca.
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Abstract

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A five-dimensional deterministic model is proposed for the dynamics between HIV and another pathogen within a given population. The model exhibits four equilibria: a disease-free equilibrium, an HIV-free equilibrium, a pathogen-free equilibrium and a co-existence equilibrium. The existence and stability of these equilibria are investigated. A competitive finite-difference method is constructed for the solution of the non-linear model. The model predicts the optimal therapy level needed to eradicate both diseases.

Type
Research Article
Information
The ANZIAM Journal , Volume 45 , Issue 2 , October 2003 , pp. 181 - 193
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Anderson, R. M. and May, R. M., Infectious diseases of humans (Oxford Univ. Press, London, 1991).CrossRefGoogle Scholar
[2]Blower, S., Koelle, K., Kirschner, D. and Mills, J., “Live attenuated HIV vaccines: predicting the trade-off between efficacy and safety”, Proc. Natl. Acad. Sci. USA 98 (2001) 3618–3623.CrossRefGoogle Scholar
[3]Diekmann, O., Heesterbeek, P. J. A. and Metz, J. A. J., “On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations”, J. Math. Biol. 28 (1990) 365–382.CrossRefGoogle ScholarPubMed
[4]Gumel, A. B., Loewen, T. D., Shivakumar, P. N., Sahai, B. M., Yu, P. and Garba, M. L., “Numerical modelling of the perturbation of HIV-1 during combination anti-retroviral therapy”, Compur. Biol. Med. 31 (2001) 287–301.CrossRefGoogle ScholarPubMed
[5]McLean, A. R. and Nowak, M. A., “Models of interactions between HIV and other pathogens”, J. Theorer. Biol. 155 (1992) 69–86.CrossRefGoogle ScholarPubMed
[6]Mickens, R. E., Applications of non-standard finite-difference schemes (World Scientific, Singapore, 2000).CrossRefGoogle Scholar
[7]Perelson, A. S. and Nelson, P. W., “Mathematical analysis of HIV-1 dynamics in vivo”, SIAM Rev. 41 (1999) 3–44.CrossRefGoogle Scholar
[8]Velasco-Hernandez, J. X., “A model for Chagas disease involving transmission by vector and blood transfusion”, Theoret. Population Biol. 46 (1994) 1–31.CrossRefGoogle Scholar