Use of generating functions in HIV/AIDS transmission models
Abstract
This study is concerned with the mathematical modeling for human immunodeficiency
virus (HIV) transmission epidemics. The mathematical models are specified by stochastic
differential equations. The differential equations are solved by use of Generating
Functions (GF).In the process of literature review, a conceptual framework is drawn
which summarizes the literature on HIV / AIDS transmission epidemic models. 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) are developed and the expectations and
variances of Susceptible (S) persons, Infected (I) persons and AIDS cases found. It
is shown from the combined model that MTCT and Heterosexual models are special
cases of the combined model.
General aspects of modeling HIV/AIDS are described in chapter 1, Chapter 2 focuses
on the literature review. MTCT model.is formulated in chapter 3. Heterosexual model
is developed in chapter 4, Chapter 5 focuses on the development of the Combined
model. Chapter 6 concludes the study.
Citation
Masters of Science in Industrial MathematicsSponsorhip
University of NairobiPublisher
Department of Mathematics University of Nairobi