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

Abstract

In this work, dynamics between uninfected cells, HBV infected cells, HDV infected cells and HBV-HDV coinfected cells are studied, 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 coinfected populations, and to the case when there is an infected cell proliferation. Optimal control theory is applied to these two systems. Seeking to reduce the infected groups and increase the number of uninfected hepatocytes, two control functions are introduced in the two mathematical models, representing two types of treatments. In fact, the main goal of this work is to discuss the effectiveness 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, lamivudine, adefovir and entecavir. The optimal controls are characterized in terms of the optimality system, which is solved numerically using an iterative method with a progressive-regressive RungeKutta fourth order scheme with a change of several parameters.

On the Impact of Awareness Programs in HIV/AIDS Prevention: An SIR Model with Optimal Control

“…This smallness restriction on the length on the time interval is due to the opposite time orientations of (16)(17)(18) and (19)(20)(21), (22), the state problem has initial values and the adjoint problem has final values. This restriction is very common in control problems [18,19,20,21,22,23,24].…”

Optimal duration and dosage of BCG intravesical immunotherapy: A free final time optimal control approach

“…Many optimal control strategies have been proposed for highlighting the advantage of optimization of some parameters in some biomathematical models . In this context, some applied mathematicians advise to rely dosage problems; also, on their optimal control approaches, they see beneficial for developing therapeutic strategies that aim to reduce tumor volume with lesser side‐effects, see, for instance, in the case of chemotherapy, the work in Yegorov and Todorov, and in the case of immunotherapy, papers in Hamdache et al…”

“…Many optimal control strategies have been proposed for highlighting the advantage of optimization of some parameters in some biomathematical models. [9][10][11] In this context, some applied mathematicians advise to rely dosage problems; also, on their optimal control approaches, they see beneficial for developing therapeutic strategies that aim to reduce tumor volume with lesser side-effects, see, for instance, in the case of chemotherapy, the work in Yegorov and Todorov, 12 and in the case of immunotherapy, papers in Hamdache et al 13,14 Some research papers on mathematical medicine have developed mathematical models which describe the evolution of tumors 15,16 and analyze the different interactions between the tumor, immune-system, and treatment. 17,18 In this paper, we formulate a minimization problem from which we aim to find the optimal dose and duration of the BCG immunotherapy procedure in the case of superficial bladder cancer, based on a prevalidated mathematical model 19 in the form of 4 ordinary differential equations which describe the superficial bladder tumor-immune interactions after the injection of BCG in the bladder of a hypothetical patient.…”

On the analysis of a multi-regions discrete SIR epidemic model: an optimal control approach

“…We will use this approach to formulate the model considered in this paper. Optimal control theory is well used as an available and effective option for diseases control, mainly Tuberculosis [16][17][18][19][20], Malaria [21,22], HIV [23][24][25][26][27][28][29][30][31], Hepatitis [32,33], Vector borne diseases [34], Cancer [35][36][37][38][39][40], and other diseases [41][42][43][44][45][46][47], but there are very few applications with both space and time as discrete variables.…”