Deterministic SIR Model of Hepatitis B Virus Infection and the Impact of Vaccination (The Case of Sunyani Municipality)
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Date
JUNE 2015
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Abstract
Deterministic SIR Models with essential factors such as Susceptible, Infective
and Removal was formulated. This is to understand the Mechanisms of Hepatitis
B Virus Infections in the Sunyani Municipality. Deterministic SIR Model
without and with Demographic turn-over were respectively used to understand
HBV Epidemic and Endemic situation of the population. An SIR Vaccination
Model was included to assess the impart of Vaccination. In the first Model,
the Reproductive Number was estimated as R0 = 1:957 > 1 which shows
epidemic population. The Model indicated that, modeling with 10 susceptible
with an infective, about 90% of the population would be infected during the
period of epidemic. The Reproductive Number for the second Model was
estimated as R0 = 1:022 which shows an endemic population. This Model
has two equilibrium states; the disease-free equilibrium state and the endemic
equilibrium state. The two equilibrium states were found to be Asymptotically
Stable. The Vaccination Model shows a decrease in the Infective whiles the
group to which Vaccination was given increased. The Reproductive Number
(R ) was estimated as R = 0:511<1.The study shows that Infectious Rate
and Reproductive Number play important roles in prevalence of disease in the
population. Our findings show that an increase in Infectious rate produces
R0 > 1 whiles a decrease in Infectious rate produces R0 < 1. Per the data from
Sunyani Municipal Hospital, an Infectious rate of at most 1% and Vaccination
rate of at least 60% can curb the situation and eventually eradicate HBV
Infection in the Municipality.
This thesis was written using LaTex Platform whiles MATLAB Code was used
for the programming.
Description
A thesis submitted to the Department of Mathematics,Kwame Nkrumah University of Science and Technology in
partial fulfillment of the requirement for the Degree
of Master of Science in Industrial Mathematics.