# American Institute of Mathematical Sciences

doi: 10.3934/naco.2020031

## Optimal control of viral infection model with saturated infection rate

 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 Published  May 2020

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.

Citation: Jaouad Danane. Optimal control of viral infection model with saturated infection rate. Numerical Algebra, Control & Optimization, doi: 10.3934/naco.2020031
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The uninfected cells as function of time
The infected cells as function of time
The viral load as function of time
The CTL cells as function of time
The optimal control $u_1$ (left) and the optimal control $u_2$ (right) versus time
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