Optimal Control of a Cell-to-Cell Fractional-Order Model with Periodic Immune Response for HCV

Xue Yang,Huijia Li,Yongmei Su,Xinjian Zhuo

doi:10.3390/sym13112121

Abstract

In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given; one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value; therefore, it is worth trying to use combination therapy to treat HCV infection.

Highlights

Hepatitis C virus (HCV), which is an enveloped flavivirus [1], causes both acute and chronic infection
It is reported that about 290,000 people have died of HCV infection so far; most of them from liver cirrhosis and hepatocellular carcinoma [2]
Understanding the mechanism of HCV virus infection is very important for the treatment of HCV

Summary

Introduction

Hepatitis C virus (HCV), which is an enveloped flavivirus [1], causes both acute and chronic infection. The mortality rates of uninfected cells, infected cells and CTLs are d1x, ay and bz respectively. The mortality rate of x, y, v and z are d1x, ay, γv and bz, respectively This model is not fractional-order and p is a constant. This system did not consider the control of drugs. It should be noted that the model (2) described the process of free virus infecting normal cells using bilinear incidence βxv, and so did paper [17,20,21,22,23]. Based on the above discussion, in order to better explain the phenomenon of HCV clinical treatment, we consider an HCV cell-to-cell fractional-order system with the saturation incidence rate. Numerical simulation and discussion are carried out in part 6, and in part 7, we give the conclusion

Preliminaries

Optimal Control Problem

Findings

Simulation and Discussion

Conclusions