Effects of combination of therapies on chronic hepatitis B virus through resolution of an optimal control problem using comparative of direct method and Pontryagin's maximum principle

This paper aims at using direct approach and Pontryagin's maximum principle to solve a hepatitis B virus dynamics optimal control problem. The controls consist of combination therapy of two treatments. The numerical implementation is done using MATLAB packages. Comparative results from these two methods show they are so close in optimal trajectories of determinant variables. Furthermore, both numerical methods are in good agreement with experimental data. In particular, combination of two treatments controls hepatitis B virus to ensure healthy.