An Extended Mathematical Model For SIV To HIV From Chimpanzees To Human
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Date
2017-02
Authors
Sule, Amiru
Journal Title
Journal ISSN
Volume Title
Publisher
Universiti Sains Malaysia
Abstract
The purpose of this study is to investigate the transmission dynamics of SIV=HIV
in humans, in the presence of chimpanzees that harbor Simian Immunodeficiency Virus
(SIV) and to suggest some control strategies in sub-Saharan Africa. SIV was believed
by some scientists to have ignited the emergence of HIV. This could be one of the reasons
that make the disease endemic in sub-Saharan Africa where these chimpanzees
are predominantly found. A basic model that consists of human and chimpanzee populations
were formulated and the equilibrium points were determined. It was obtained
that the disease free equilibrium point is locally asymptotically stable when the basic
reproduction number is found to be less than unity and unstable otherwise. The model
is extended to consider the effects of control strategies. Sensitivity analysis was carried
out to obtain the most sensitive parameters that help most in disease spread. The
result shows that the contact rate of susceptible human with the infected human and
the contact rate of susceptible chimpanzees with infective chimpanzees are the most
sensitive parameters. Some control parameters (condom use, treatment and culling)
were considered in order to control the spread of the disease. The basic model was
further extended to consider the effects of vertical transmission (mother to child) on
both populations on the spread of the virus. Some basic properties of the extended
model were investigated and basic reproduction number was computed using Next
Generation Operator method. Sensitivity analysis of the model parameters was carried out and Pontryagin’s Maximum Principle is applied with some control parameters of (HIV testing, treatment and culling) to reduce the infective classes of human and chimpanzees with minimal intervention funds.
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Keywords
An extended mathematical model for SIV to HIV , from chimpanzees to human