Unconditionally Stable Numerical Scheme to Study the Dynamics of Hepatitis B Disease

Abstract

Hepatitis B is a contagious liver infection caused by hepatitis B virus and is a worldwide public health problem. According to WHO about 350 million people are suffering from this chronic disease. Therefore millions of peoples are at stack of cirrhosis, hepatocellular carcinoma, and cancer of liver or even liver failure. Hepatitis B still has necessary complex issues that must be addressed effectively. In this research paper, we have developed NSFD scheme for HBV model. The simulations show that our proposed NSFD scheme gives stable, unconditional, positive and converging results at all step sizes as compared to the traditional RK-4 method and Euler method which diverge at large step sizes and produce negative and unstable results with large oscillations.Later we have analyzed the local asymptotic stability of this proposed NSFD scheme using Linearized Stability Theorem and Schur-Cohn Stability Criteria.