Mathematical modelling of the optimal control of hepatitis b virus (HBV) infection in the presence of cytotoxic cells

A non-linear mathematical model is formulated and analysed to study the optimal control of HBV infection in the presence of cytotoxic cells. The proposed model describes the interaction between normal cells, HBV and cytotoxic cells. The goal is to maximize the number of normal cells by evaluating the impact of optimal control strategies mainly treatment and preventions activities in terminating or restricting the spread of the disease. In this study, the optimal control is obtained by solving the optimality system which is composed of nonlinear ODEs with initial conditions and nonlinear adjoint ODEs with transversality conditions. Also numerical simulations and sensitivity analysis are carried out to determine key parameters contributing to the spread of the disease and to illustrate analytical results. A sensitivity analysis shows that the control variable, which represents the efficiency of preventions activities, is the most sensitive parameter and the least is death rate of HBV due to treatment. The result of the study shows that, application of optimal control in the presence of cytotoxic cells decreases the spread of HBV infection.