Analysis of Vertical Transmission Dynamics of Infectious Hepatitis B Virus: Mathematical Model Involving Vaccination And Treatment in Turkana County, Kenya
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Date
2022
Authors
Ghai Kuei, Geu
Journal Title
Journal ISSN
Volume Title
Publisher
Kenyatta University
Abstract
Hepatitis B has been a major global health menace for it is a potentially life-threatening liver
disease. Close to 0.25 billion persons are living with this infectious disease across the world.
It’s transmitted by infected individual to uninfected person either vertically (transmission
before or during birth by carrier mother to the baby) or horizontally (transmission when the
bodily fluid of an infected person comes into contact with the hepatitis B virus-free person).
This can happen through the sharing of non-sterilized injection syringes, tattooing objects and
through sexual intercourse. This particular project studied a mathematical model that
combined both vaccination and treatment as a means to controlling the hepatitis B virus
(HBV). In our mathematical model, equations are derived from the flow chart representing the
HBV transmission dynamics. The determination of the disease-free equilibrium state (DFE),
the endemic equilibrium state (EE) and the basic reproduction number 𝑅0 were made. The
stability of these points were determined and the results show that the disease-free
equilibrium was both locally and globally asymptotically stable. In other words, 𝑅0 < 1. The
stability analysis of endemic equilibrium point also reveals that the point is locally and
globally asymptotically stable, that is, 𝑅0 > 1. The basic reproduction number 𝑅0 is
computed using the next generation matrix method. The system of ordinary differential
equations (ODEs), which is non-linear are solved by numerical simulation. This was achieved
by use of Runge-kutta method of order four with the help of MATLAB software. These results
show that either of the method, treatment or vaccination, administered is effective in
alleviating the spread of HBV disease. However, when both control strategies are combined,
the disease is quickly controlled and ultimately brought to eradication.
Description
A Research Project Submitted In Partial Fulfilment of the Requirements of the Award Of The
Degree of Master of Science in Applied Mathematics in the School of Pure and Applied
Sciences of Kenyatta University, August, 2022
Keywords
Vertical Transmission Dynamics, Infectious, Hepatitis B Virus, Mathematical Model, Vaccination, Treatment, Turkana County, Kenya