Optimal control of viral infection model with saturated infection rate

Jaouad Danane

doi:10.3934/naco.2020031

Article Contents

2021, Volume 11, Issue 3: 363-375. Doi: 10.3934/naco.2020031

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Optimal control of viral infection model with saturated infection rate

Jaouad Danane

Laboratory of Mathematics and Applications, Faculty of Sciences and Techniques, Hassan II University of Casablanca, PO Box 146, Mohammedia, Morocco

Received: November 2019

Revised: February 2020

Early access: May 2020

Published: September 2021

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Abstract

This paper deals with an optimal control problem for a viral infection model with cytotoxic T-lymphocytes (CTL) immune response. The model under consideration describes the interaction between the uninfected cells, the infected cells, the free viruses and the CTL cells. The two treatments represent the efficiency of drug treatment in inhibiting viral production and preventing new infections. Existence of the optimal control pair is established and the 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 performed in order to show the role of optimal therapy in controlling the infection severity.

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Mathematics Subject Classification: 92B05, 93C95, 34H05, 65L03.

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Figure 1. The uninfected cells as function of time

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Figure 2. The infected cells as function of time

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Figure 3. The viral load as function of time

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Figure 4. The CTL cells as function of time

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Figure 5. The optimal control $ u_1 $ (left) and the optimal control $ u_2 $ (right) versus time

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