Optimal control of an HIV model with CTL cells and latently infected cells

Abstract

This paper deals with an optimal control problem for an human immunodeficiency virus (HIV) infection model with cytotoxic T-lymphocytes (CTL) immune response and latently infected cells. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively 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 minimum 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.

Optimal control of viral infection model with saturated infection rate

“…Our model uses a more realistic saturated incidence function 8,23,24]. This saturated incidence functional describes the infection rate taking into consideration the effect of free viruses crowd near the healthy cells.…”

Mathematical analysis and simulation of a stochastic COVID-19 Lévy jump model with isolation strategy

“…Infectious diseases modeling has captivated the interest of many research works during the last recent years [1] , [6] , [2] , [3] , [4] , [5] , [7] . The basic SIR model representing the dynamics behavior of the three main populations that represent the susceptible , the infected and the recovered , was firstly proposed in 1927 by Kermack and Mc Kendricks [8] ; the suggested model has played an important role in starting different research works in disease dynamics field.…”

“…Understanding the interaction dynamics between the different infection components becomes then an important issue to prevent many serious infectious disease outbreaks. For instance, several mathematical models have been used to better understand the behavior of various viral infections, such as the hepatitis B virus (HBV) [6] , [10] , [9] , [11] , [12] human immunodeficiency virus (HIV) [1] , [14] , [2] , [13] , [15] , [3] , [4] or hepatitis C virus (HCV) [16] , [19] , [18] , [17] .…”

Controllability of nonlinear fractional evolution systems in Banach spaces: A survey

“…For the sake of using fixed-point theorem, the controllability problem of nonlinear systems is transformed to a fixed-point problem of corresponding nonlinear operator in a appropriate function space. Frequently used fixed-point theorems include Banach's fixed-point theorem [12], Schauder's fixed-point theorem [21,29,129], Darbo's fixed-point theorem [16,26], Schaefer's fixed-point theorem [16], Krasnoselskii's fixed-point theorem [59,100,116], Sadovskii's fixed-point theorem [40,68,122], Mönch's fixed-point theorem [14,32,54,123,125], etc. It should be particularly noted that the controllability of fractional evolution systems (FESs) is an important issue for lots of practical problems since the fractional calculus can derive better results than integeral order one.…”

“…Therefore, various dynamic behaviors of FESs with time delay have been investigated during the last few decades, such as optimal controllability, stability and stabilization problems. With the continuous development of fractional calculus, more and more attention has been paid to the controllability of various kinds of FESs with time delay in recent years [12,14,24,29,123]. In addition, there is another inevitable factor in practice, that is, the phenomenon of impulse which widely exists in the real world.…”