Modeling and control of the hepatitis B virus spreading using an epidemic model

Abstract

Abstract We describe the formulation of hepatitis B epidemic model with saturated incidence rate. Once we formulate the epidemic problem then we discuss the basic properties (existence of positive solutions and positively invariant set etc.) to show the mathematical as well as the biological feasibility. We find the basic reproduction number R0. The disease free and endemic equilibria of the model will be obtained to investigate the local stability and backward bifurcation. We also perform the local sensitivity analysis and find the sensitive parameter. On the basis of this, we develop the optimal control strategy for the elimination of hepatitis B virus (HBV) spreading with the help of optimization theory. Finally, a large scale numerical simulation will be performed to verify our analytical findings.