Contribution Of Vaccination And Treatment In Reduction Of Re-Infection Of Hbv Disease: A Mathematical Model Analysis And Numerical Simulation
Abstract
Firaol Asfaw Wodajo, Asfaw Wodajo Nigussie, Chalsiste Asfaw Wodajo, Tirunesh Wolde Dera
Hepatitis B is a globally infectious disease. HBV-reinfection after HBV-related liver transplantation is a frequent clinical problem. The risk of HBV-reinfection directly correlates with the viral load before liver transplantation. If reinfection does occur in most cases the course of the disease is enhanced compared to the situation before transplantation. The progression of HBVrelated liver disease is accelerated starting 2 months after transplantation and r in re-transplantation or death of the patients. Mathematical modeling of HBV transmission is an interesting research area. In this paper, we present characteristics of HBV virus transmission in the form of a mathematical model. We proposed and analyzed a compartmental nonlinear deterministic mathematical model SVEIRE for transmission dynamics and control of Hepatitis B virus disease. In this model, we used force infection which takes the contact rate of susceptible population and transmission probability into account. We proved that the solution of the considered dynamical system is positive and bounded. The model is studied qualitatively using the stability theory of differential equations and the basic reproductive number that represents the epidemic indicator is obtained from the largest eigenvalue of the next-generation matrix. Both local and global asymptotic stability conditions for disease-free and endemic equilibria are determined. Sensitive analysis results show that enhancing the vaccination rate for newborns and treatment for chronically infected individuals is very effective to stop the transmission of HBV. It is also shown that re-infection of HBV plays a great role in increasing the number of infected populations. Finally, this paper depicts combination of vaccination and treatment that will be the most useful way to control Hepatitis B virus infection.