On Effectiveness of an Optimal Antiviral Bitherapy in HBV-HDV Coinfection Model

In this work, dynamics between uninfected cells, HBV infected cells, HDV infected cells and HBV-HDV coinfected cells are stud-ied, based on two systems of four ordinary differential equations. The two pre-validated differential systems which are considered in this paper, are respectively associated to the case when there is no infected cell proliferation of HBV, HDV and HBV-HDV coin-fected populations, and to the case when there is an infected cell proliferation. Optimal control theory is applied to these two sys-tems. Seeking to reduce the infected groups and increase the num-ber of uninfected hepatocytes, two control functions are introduced in the two mathematical models, representing two types of treat-ments. In fact, the main goal of this work is to discuss the effec-tiveness of an antivial bitherapy that could include any inhibitor for HDV infection such as lonafarnib, with other classical treatments often used against HBV infection such as interferons, lamivu-dine, adefovir and entecavir. The optimal controls are character-ized in terms of the optimality system, which is solved numerically using an iterative method with a progressive-regressive Runge-Kutta fourth order scheme with a change of several parameters