Optimal Control of a Delayed Hepatitis B Viral Infection Model with DNA-Containing Capsids and Cure Rate
We present in this paper a delay-differential equation model that describes the interactions between hepatitis B virus (HBV) with DNA-containing capsids and liver cells (hepatocytes). Both the treatments, the intracellular delay and the cure rate of infected cells, are incorporated into the model. The first treatment represents the efficiency of drug treatment in preventing new infections, whereas the second stands for the efficiency of drug treatment in inhibiting viral production. Existence for the optimal control pair is established, Pontryagin’s maximum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward difference approximation. Finally, numerical simulations are established to show the role of optimal therapy in controlling viral replication.
KeywordsHBV infection Delay Optimal control Numerical simulation
- 12.X. Zhou, X. Song, X. Shi, A differential equation model of HIV infection of CD4+ T-cells with cure rate. J. Math. Anal. Appl. 342,(2), 1342–1355 (2008)Google Scholar
- 14.D.L. Lukes Differential Equations: Classical to Controlled. Mathematics in Science and Engineering (Academic Press, New York, 1982), p. 162Google Scholar
- 16.K. Hattaf, N. Yousfi, Optimal control of a delayed HIV infection model with immune response using an efficient numerical method. ISRN Biomath. 2012 (2012). https://doi.org/10.5402/2012/215124
- 19.K. Manna, Global properties of a HBV infection model with HBV DNA-containing capsids and CTL immune response. Int. J. Appl. Comput. Math. (2016). https://doi.org/10.1007/s40819-016-0205-4
- 20.A. Meskaf, K. Allali, Y. Tabit. Optimal control of a delayed hepatitis B viral infection model with cytotoxic T-lymphocyte and antibody responses. Int. J. Dyn. Control (2016). https://doi.org/10.1007/s40435-016-0231-4