Galerkin time discretization for transmission dynamics of HBV with non-linear saturated incidence rate

Abstract

This study formulated an autonomous non-linear epidemic model for the numerical solutions of the transmission dynamics of acute and chronic hepatitis B with a saturated incidence rate, which prevailed due to the hepatitis B virus. In this article, a model of HBV is extended by introducing a non-linear saturated incidence rate. That non-linear saturated incidence rate helps to reduce the infected population by improving the immunity of the human body. The continuous Galerkin-Petrove (2) technique a numerical method, is used for finding the solution of the mentioned model. For continuous Galerkin-Petrove (2) technique, we need two variables on every step that must be figured out by solving a square matrix. Different parameters on the population dynamics of susceptible, infected with acute and chronic hepatitis B virus and recovered individuals are analyzed. As it could be seen that the increase in the value of the saturation constant (ξ1) and recovery rate from chronic stage to recovered (ψ2) led to the decrease in the population infected with acute and chronic HBV so susceptible population has large concentration and less population is contaminated and the outcomes are illustrated graphically. The model is solved by utilizing a Runge Kutta method of order (4) scheme and results of both techniques are compared numerically and graphically. Although the numerical and graphical results of both methods (continuous Galerkin-Petrove (2) and Runge Kutta method of order (4)) are the same after comparison the continuous Galerkin-Petrove (2) is more efficient and less time consuming as compared to Runge Kutta method of order (4).