The Role of Immune Response in Optimal HIV Treatment Interventions

Abstract

A mathematical model for the transmission dynamics of human immunodeficiency virus (HIV) within a host is developed. Our model focuses on the roles of immune response cells or cytotoxic lymphocytes (CTLs). The model includes active and inactive cytotoxic immune cells. The basic reproduction number and the global stability of the virus free equilibrium is carried out. The model is modified to include anti-retroviral treatment interventions and the controlled reproduction number is explored. Their effects on the HIV infection dynamics are investigated. Two different disease stage scenarios are assessed: early-stage and advanced-stage of the disease. Furthermore, optimal control theory is employed to enhance healthy CD4 + T cells, active cytotoxic immune cells and minimize the total cost of anti-retroviral treatment interventions. Two different anti-retroviral treatment interventions (RTI and PI) are incorporated. The results highlight the key roles of cytotoxic immune response in the HIV infection dynamics and corresponding optimal treatment strategies. It turns out that the combined control (both RTI and PI) and stronger immune response is the best intervention to maximize healthy CD4 + T cells at a minimal cost of treatments.

Mathematical Analysis and Numerical Solution of a Model of HIV with a Discrete Time Delay

“…To carry out the simulations we use the constructed NSFD numerical scheme (34). We choose the parameter values based on existing experimental data and previous model studies, see [54,106,111,112]. The values of these parameters are given in Tables 1 and 2.…”

A Multi-Scale Model for the Spread of HIV in a Population Considering the Immune Status of People

“…The model (7) was proposed in [23], but its local stability was not analyzed with control; here, we perform this analysis and use it to describe the immune system of each person in the complex network.…”

“…During the last two decades, there has been an increase in the study and use of complex networks in different contexts [15][16][17][18][19][20][21][22]; particularly, complex networks have gained strength when representing sexual contacts among people. We, herein, introduce a model that uses complex networks to study the dynamics of HIV propagation in people between 15 and 24 years of age, who interact through sexual contacts, considering at the same time the dynamics of infection in the immune system of each young person; the immune system is modeled through the system of ordinary differential Equations (ODE) proposed in [23]. The research gains importance by being a multi-scale model that integrates two components: the population (network) and the immunological (ODE system) because the population dynamics cannot be detached from the immunological, thus, adding to previous research that studies both components separately.…”

“…The intervals were assumed randomly and obtained from [17,27]. A mathematical model that considers the dynamics of the HIV infection while using ART has been described in [23], which will be used in this work. The following describes the model and the Appendix A contain proofs for the local stability analysis.…”