Mathematical Model and Study of Viral Hepatitis among Population in Afghanistan

Abstract

Despite availability of strategies against viral hepatitis, it is still a serious disease, which millions of people are already infected with, hence it yet needs to be focused on. As an attempt, we formulated a single mathematical model describing behaviour of all strains of viral hepatitis, presented in the literature. The basic reproduction number(R_0) at disease free equilibrium point is computed, feasible region has been determined. For local stability of the model, R_0 has been taken into account and for global stability of the model Lyapunov method is followed. The model is then applied to the data available for Afghanistan for the year 2020. Based on the data, values of the parameters are estimated, using Minimum Mean Absolute Error (MAE) method. Numerical simulation is performed to support the model and then the results are plotted and represented graphically. One-at-a-time sensitivity analysis (OAT) method is used for sensitivity analysis and involved parameters have been examined for the propose of sensitivity analysis, it indicated that infection rates of acute and chronic states of viral hepatitis are the most sensitive and critical parameters. It has been observed that large number of populations can become infected followed by small increment of infection rates. It has also been noticed that, entire population of Afghanistan could become infected, if no prevention measures were taken. The model presented in this paper is useful for forecasting outbreak by viral hepatitis and it can further be modified by including prevention measures.

Keywords

• viral hepatitis, mathematical model, analysis, simulation, estimation