Optimally Controlled Treatment Strategy Using Interferon and Ribavirin for Hepatitis C

Abstract

The main goal of this paper is to determine an optimal treatment strategy using interferon and ribavirin, through mathematical modeling. We formulate a mathematical model using a system of ordinary differential equations, which describes the interaction of target cells (hepatocytes), infected cells, infectious virions, non-infectious virions and the two drugs, namely, interferon and ribavirin. We solve an optimal control problem with an objective functional that minimizes the viral load as well as the side effects of treatment. Finally we derive optimal treatment strategy and then solve it numerically.

Optimal efficacy of ribavirin in the treatment of hepatitis C

“…This work also further expands the previous work of the author [17] by incorporating a clinically validated efficacy of IFN.…”

“…This model was presented in the article of Chakrabarty and Joshi [17] and is represented by a system of coupled ordinary differential equations (ODEs). The system involves h (hepatocytes), h i (productively infected hepatocytes), v i (infectious virions) and v ni (non-infectious virions).…”

“…In the earlier work [17] we used a control theory approach to determine the optimal n I and n R . In this work we will however use a formulation of n I based on clinical observations that was presented by Powers et al [18].…”

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

“…Figures 2 and 3 report some similarities from numerical results obtained in Figure 1 but with a larger scale to show exactly what happens to x, y, z and w cells when a treatment is used against HBV infection, HDV infection, and HBV-HDV coinfection. On the other hand, it is recalled that k 1 and k 2 are used to show respectively the main roles of treatments used against HBV and HDV infection in attempt to block the viral production of B and Delta viruses, such considerations were also used by Chakrabarty et al for the optimization of a bitherapy with interferon and ribavirin against hepatitis C [11]. In fact, when k 1 and k 2 take values close to 1; k 1 = 0.8 and k 2 = 0.8 in Figures 1 and 2 for instance, a rapid decrease of infected cells with HBV or HDV or even with both viral infections, is observed, and it is also seen a rapid increase of uninfected cells compared to the case where k 1 and k 2 become to have farther values to, k 1 = 0.69 and k 2 = 0.69 in Figure 4 for instance, and where z and w cells late to decrease and taper off respectively until 150 and 130 days of treatment.…”

“…Mathematical and immunological models play an important role in the study of dynamics of infections arising from viruses. In Reference [11] the authors worked on the combination of IFN and ribavirin as a therapy for HCV. The fundamental idea in this paper is a combination of two treatments, the first treatment (resp.…”