Analysis and Simulation of a Fractional Order Optimal Control Model for HBV

Abstract

In this paper, we propose a fractional optimal control model of anti-HBV infection based on saturation incidence and logistic proliferation of uninfected cells for the first time. We derive the basic reproduction number R0 and the cytotoxic T lymphocyte immune response reproductive number R1 and give the stable analysis based on R0 and R1. We analyse the optimal control condition and give two optimal control strategies about entecavir monotherapy and combination therapy of traditional Chinese medicine and entecavir with different fractional orders by simulation. The simulation shows that combination therapy may be a good choice in anti-HBV infection therapy. We also compare the objective function values of the optimal control strategies with other constant control strategies; the comparison shows that the optimal therapy can get similar or better treatment effect with less drug dose and side effects.

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

“…Paper [27] uses Holling type-II incidence instead of bilinear incidence, that is βxv 1+mx . Yang et al [28] changed it to saturation incidence function βxv x+v , and the reproductive number is R 0 = βk µ(a+δ) , which seems more reasonable because it is independent of the number of total cells of liver. Since infected liver cells can also infect normal liver cells, it might also be better to replace βxy with βxy x+y .…”