Mathematical Modeling for Human Immunodeficiency Virus (HIV) Transmission Using Generating Function Approach

Anderson, R.M., May, R.M. (1991) Infectious diseases of humans: Dynamics and control. Oxford, UK: Oxford University Press

Anderson, R.M., May, R.M., McLean, A.R. (1988) Possible demographic consequences of AIDS in developing countries. Nature, 332(6161): 228-34

15 Pages Posted: 28 Feb 2013

See all articles by Rachel Mbogo

Rachel Mbogo

Strathmore University

Olorunsola Olowofeso

Federal University of Technology Akure (FUTA)

Date Written: February 9, 2005

Abstract

This study is concerned with the mathematical modeling for human immuno-deficiency virus (HIV) transmission epidemics. The mathematical models are specified by stochastic differential equations that are solved by use of Generating Functions (GF). Models based on Mother to child transmission (MTCT) (age group 0-5 years), Heterosexual transmission (age group 15 and more years) and combined case (incorporating all groups and the two modes of transmission) were developed and the expectations and variances of Susceptible (S) persons, Infected (I) persons and AIDS cases were found. The S1(t) Susceptible model produces a constant expectation and increasing variance. It was shown that Mother to Child transmission and Heterosexual models are special cases of the Combined model.

Keywords: Generating Function, HIV Transmission, Stochastic compartmental model, MTCT and Combined model

Suggested Citation

Mbogo, Rachel and Olowofeso, Olorunsola, Mathematical Modeling for Human Immunodeficiency Virus (HIV) Transmission Using Generating Function Approach (February 9, 2005). Anderson, R.M., May, R.M. (1991) Infectious diseases of humans: Dynamics and control. Oxford, UK: Oxford University Press . Available at SSRN: https://ssrn.com/abstract=2225479

Rachel Mbogo (Contact Author)

Strathmore University ( email )

P.O. Box 59857
Nairobi, 00200
Kenya

Olorunsola Olowofeso

Federal University of Technology Akure (FUTA) ( email )

Akure, Ondo State
Nigeria

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