Optimal Control of a Delayed Hepatitis B Viral Infection Model with DNA-Containing Capsids and Cure Rate

Adil Meskaf and Karam Allali
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Adil Meskaf: University Chouaib Doukkali, Department of SEG, Polydisciplinary Faculty
Karam Allali: University Hassan II, Department of Mathematics, Faculty of Sciences and Technologies

A chapter in Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics, 2019, pp 23-33 from Springer

Abstract: Abstract 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.

Keywords: HBV infection; Delay; Optimal control; Numerical simulation (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-23433-1_2

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DOI: 10.1007/978-3-030-23433-1_2

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