Cytotoxic Cells and Control Strategies are Effective in Reducing the HBV Infection through a Mathematical Modelling

A non-linear mathematical model is formulated and analysed to study the mathematical modelling of 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 existence of an optimal control pair is obtained. 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. Numerical studies of the model are carried out to see the effects of the key parameters on the optimal control of HBV infection in the presence of cytotoxic. The result of the study showed that application of optimal control in the presence of cytotoxic cells leads to the decrease of infection of HBV disease.

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