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

  • Adil Meskaf
  • Karam Allali
Chapter

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 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Adil Meskaf
    • 1
  • Karam Allali
    • 2
  1. 1.Department of SEG, Polydisciplinary FacultyUniversity Chouaib DoukkaliEl JadidaMorocco
  2. 2.Department of Mathematics, Faculty of Sciences and TechnologiesUniversity Hassan IIMohammediaMorocco

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