Optimal Control of Drug Therapy in a Hepatitis B Model

Abstract

Combination antiviral drug therapy improves the survival rates of patients chronically infected with hepatitis B virus by controlling viral replication and enhancing immune responses. Some of these drugs have side effects that make them unsuitable for long-term administration. To address the trade-off between the positive and negative effects of the combination therapy, we investigated an optimal control problem for a delay differential equation model of immune responses to hepatitis virus B infection. Our optimal control problem investigates the interplay between virological and immunomodulatory effects of therapy, the control of viremia and the administration of the minimal dosage over a short period of time. Our numerical results show that the high drug levels that induce immune modulation rather than suppression of virological factors are essential for the clearance of hepatitis B virus.

Mathematical Modeling of the Adaptive Immune Responses in the Early Stage of the HBV Infection

“…The optimal control of the HBV therapy aims to find the optimal strategy of the drugs that allow blocking the virus production and infection. Several papers studied the optimal control of the HBV therapy [16,[20][21][22]. In our case, the therapy will have an antiviral effect, and we ignore its immunomodulatory effect since we do not know what impact the use of the therapy could have on the immune system in the early stage of HBV infection.…”

Modeling the dynamics of hepatitis B infection, immunity, and drug therapy

“…Assuming that the virus follows the dynamics of chronic HBV (for the parameters obtained by fitting the data of patient 7 in Figure ), Forde et al. have investigated whether the timing and the type of IFN effects are important in the success of the treatment . To determine that, they set up an optimal control problem, where parameters [ ϵ ] and [ η ] are assumed to be time‐dependent, u 1 ( t ) and u 2 ( t ).…”

“…Others estimated the efficacy of mono‐ and combination drug therapy, the virological‐immunological mechanisms associated with the therapy, and the role of immune responses in HBV DNA removal . Last, they predicted optimal regimes of combination therapy …”

Um modelo matemático para Hepatite B de ordem fracionária

“…Os parâmetros biológicos utilizados no modelo para realizar as simulações estão descritos na Tabela 1 [8,9]. Além disso as condições iniciais são T (0) = 1 × 10 −3 , I(0) = 9 × 10 −4 , V (0) = 3.07 × 10 −4 , os parâmetros numéricos h = 0.1, µ = 3, para a função denominador ϕ(h, µ + 1) e o tempo total de simulação foi de 500 dias.…”

“…No Brasil, cerca de 15% da população já foi contaminada com o vírus e 1% das pessoasé portadora crônica da doença [8,9] .É transmitida pelo vírus HBV, que causa irritação e inflamação do fígado. Sua transmissão pode ocorrer por meio de relações sexuais e transmissão sanguínea.…”