Optimal control of a delayed HIV model

We propose a model for the human immunodeficiency virus type 1 (HIV-1) infection with intracellular delay and prove the local asymptotical stability of the equilibrium points. Then we introduce a control function representing the efficiency of reverse transcriptase inhibitors and consider the pharmacological delay associated to the control. Finally, we propose and analyze an optimal control problem with state and control delays. Through numerical simulations, extremal solutions are proposed for minimization of the virus concentration and treatment costs.publishe

Dynamics of a Stochastic Viral Infection Model with Immune Response

The aim of this work is to study the dynamical behavior of a stochastic viral infection model which is formulated by four nonlinear stochastic differential equations to describe the interactions between virus, host cells, and immune response represented by cytotoxic T lymphocytes (CTL) cells. The infection transmission process is modeled by Hattaf-Yousfi incidence function which includes many special cases existing in the literature. The positivity of solutions is investigated. In addition, the extinction of the infection is established in terms of the basic reproduction number R0. Moreover, sufficient conditions for the fluctuation of solutions around the two infection equilibria are obtained. Numerical simulations are presented to illustrate our theoretical results

Reducing the Latent CD4

In HIV infection, the latent cells represent a reservoir that contributes to the failure of the Highly Active Anti-Retroviral Therapy (HAART). This fact requires investigating the possible strategy to improve the administration of the HAART therapy, in order to guarantee the control of the virus load to the lost level as long as possible. In this work, we aim to study the possibility of reducing the latent infected CD4+ reservoir in the HIV infection by considering a mathematical model of two types of latently infected CD4+: fast and slow, and eight virus strains: wild-type, three single mutants, three double mutants and a fully resistant triple mutant. The HAART therapy is considered as an optimal control problem that aimes to reduce the virus load and the infected cells. Our optimal control approach shows the impact of the optimal HAART therapy on reducing two different types of the reservoirs of the latent infected CD4+ cells

On SICA models for HIV transmission

We revisit the SICA (Susceptible-Infectious-Chronic-AIDS) mathematical model for transmission dynamics of the human immunodeficiency virus (HIV) with varying population size in a homogeneously mixing population. We consider SICA models given by systems of ordinary differential equations and some generalizations given by systems with fractional and stochastic differential operators. Local and global stability results are proved for deterministic, fractional, and stochastic-type SICA models. Two case studies, in Cape Verde and Morocco, are investigated.publishe