April 8, S1793524511001192
2011 12:14 WSPC
S1793-5245
242-IJB
International Journal of Biomathematics Vol. 4, No. 1 (March 2011) 75–92 c World Scientific Publishing Company DOI: 10.1142/S1793524511001192
EXPLORING THE EFFECTS OF PARAMETER HETEROGENEITY ON THE INTRINSIC DYNAMICS OF HIV/AIDS IN HETEROSEXUAL SETTINGS
E. T. NGARAKANA-GWASIRA∗ , C. P. BHUNU†,¶ , S. MUSHAYABASA† , S. D. HOVE-MUSEKWA† , W. GARIRA‡ and J. M. TCHUENCHE§ ∗Department of Mathematics, University of Zimbabwe P. O. Box MP 167 Mount Pleasant, Harare, Zimbabwe †Department
of Applied Mathematics, National University of Zimbabwe P. O. Box AC 939 Ascot, Bulawayo, Zimbabwe
‡Department
of Mathematics and Applied Mathematics University of Venda, South Africa
§Department
of Mathematics and Statistics University of Guelph, Guelph, ON N1G 2W1 Canada ¶
[email protected] ¶
[email protected]
Received 15 October 2009 Revised 10 March 2010 A sex-structured staged progression model for heterosexual transmission dynamics of HIV/AIDS in a community to theoretically assess the effects of gender parameter accounting for population heterogeneity is formulated and analyzed. The basic model without this parameter is analyzed, and then extended to include gender heterogeneity in order to explore its role on the transmission dynamics of the disease. Mathematical properties including epidemic thresholds known as reproductive numbers are derived. The models are numerically analysed using some demographic and epidemiological parameters for Zimbabwe. These simulations suggest that the use of identical gender attributes simplifies computation at the expense of reality as it underestimates the size of the epidemic by 5%. This study demonstrates that the use of gender related parameter in the transmission dynamics of HIV gives a better estimate of the prevalence of the epidemic and should be given prominence. Keywords: HIV/AIDS model; gender; stability; parameter heterogeneity.
1. Introduction HIV is a major burden in most populations within sub-Saharan Africa. It is one of the World’s biggest killers of children and young adults, the vital age groups that countries can ill-afford to lose. Sub-Saharan Africa has continued to bear the brunt ¶ Corresponding
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