Analysis of Vertical Transmission Dynamics Of Infectious Hepatitis B Virus: Mathematical Model Involving Vaccination and Treatment
- October 29, 2021
- Posted by: rsispostadmin
- Category: IJRIAS
International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume VI, Issue X, October 2021|ISSN 2454-6194
Geu Ghai Kuei, J.K. Gatoto
Kenyatta University, Kenya
Abstract: Hepatitis B has been a major global health menace for it’s a potentially life-threatening liver disease. Around two 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. We determined the disease-free equilibrium (DFE) state, the endemic equilibrium (EE) state and the basic reproduction number . The stability of these points are determined and the results show that the disease-free equilibrium is both locally and globally asymptotically stable i.e . The stability analysis of endemic equilibrium point also reveals that the point is locally and globally asymptotically stable, i.e . The basic reproduction number is computed using the next generation matrix method. The systems of ordinary differential equations (ODEs), which are 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 and techniques. 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.
Keywords: Mathematical model, Hepatitis B Virus (HBV), Treatment, Reproduction number, stable, unstable, Disease-free Equilibrium and Endemic Equilibrium
I.INTRODUCTION
1.1 Background Information
Hepatitis B Virus (HBV) is a hepadnavirus with circular genome composed of partially double-stranded DNA and replicates through intermediate form by reverse transcription, Lacamini (2004). Hepatitis B therefore, is a liver infection caused by HBV and always finally evolves to liver cirrhosis and hepatocarcinom, Klysik (2001). This disease has two
