Solving an optimal control problem of hepatitis B virus dynamics: Efficacy of fuzzy logic strategy

Abstract

This work aims at using fuzzy logic strategy to solve a hepatitis B virus (HBV) optimal control problem. To test the efficacy of this numerical method, we compare numerical results with those obtained using direct method. We consider a patient under treatment during 12 months where the two drugs are taken as controls. The results are rather satisfactory. In particular, the reaction of HBV to drugs can be modeled and a feedback can be approximated by the solution of a linear quadratic problem. The drugs reduce the risk of HBV. Furthermore, results of both numerical methods are in good agreement with experimental data and this justifies the efficacy of fuzzy logic strategy in solving optimal control problems.

Perturbation Iteration Method Compared with Direct Method and Fuzzy Logic Strategy for Solving An Optimal Control Problem of An Uninfected Hepatitis B Virus Dynamics

“…Thus, the solution of optimal control problem (4), equations ( 1)-( 3) can be solved using different mathematical methods. In [18], the details about discretization, numerical solution of direct methods and approach integrating fuzzy logic are described. In this work, we focus on the perturbation iteration method.…”

“…The starting value of the controls u 1 and u 2 is 1 if treatment is absent and is 0 in the case of maximal use of therapy. To investigate the efficacy of the perturbation iteration method, the numerical results implemented using this method are compared with one calculated by the direct method and fuzzy logic strategy [18]. Figures 1 and 2 illustrate the numerical simulation results.…”

“…This is an advantage of this method. Refer to [18] for the details of direct methods and approaches integrating fuzzy logic. This paper focuses on describing the algorithm of the perturbation iteration method.…”

Mathematical Model of Hepatitis B Disease with Optimal Control and Cost‐Effectiveness Analysis

“…And simulation of their results showed that combining these three interventions at the same time is beneficial and efficient for controlling hepatitis B infection. Other researchers such as [11][12][13][14][15] have also studied on dynamics of hepatitis B disease with optimal controls. In this work, we suggested a model for hepatitis B disease adopted from [8], including a two-dose vaccine series class, and extended it to an optimal control model to study the cost-effectiveness analysis, which was not studied by the mentioned researchers above.…”