Mathematical modeling of HIV-1 therapeutic initiatives: shock and kill strategy in the brain and the natural control of the virus in the plasma

Abstract

This thesis is based on four main studies. The first two studies present a detailed methodology for completing dynamical system parameter estimation using Bayesian inference. The next two studies are about using this methodology to investigate critical human immunodeficiency virus-1 therapeutic initiatives: “Shock and Kill” strategy in the brain and the natural control of the virus in the plasma. The first study in this thesis is based on the 2020 paper “Bayesian inference for dynamical systems” in the journal Infectious Disease Modelling. This paper described a comprehensive methodology for dynamical system parameter estimation using Bayesian inference and it covered the topics of utilizing different distributions, Markov Chain Monte Carlo (MCMC) sampling, obtaining credible intervals for parameters, and prediction intervals for solutions. It also included a logistic growth example to illustrate the methodology. This study is described in Chapter 2. The next study in this thesis is about the first MATLAB implementation of the Diffusive Nested Sampling (DNS) algorithm called “MatlabDiffNestAlg”, which is available to the community on the MATLAB Central File Exchange and uploaded into the CERN supported repository Zenodo. DNS is a Bayesian inference method that is capable of reliably estimating parameters in a high dimensional space. The DNS algorithm is also able to effectively sample from multimodal distributions and it provides samples that are estimates of the actual posterior density. Chapter 3 describes the DNS algorithm, and the MATLAB implementation of the DNS algorithm is explained in Section 3.C. The third study in this thesis is based on the 2021 paper “Modeling the effects of latency reversing drugs during HIV-1 and SIV brain infection with implications for the “Shock and Kill” strategy” in the Bulletin of Mathematical Biology. This was the first mathematical model to qualitatively analyze the dynamics of latently and productively infected cells in the brain during human immunodeficiency virus-1 (HIV-1) and simian immunodeficiency virus (SIV) infection and to quantify the size of the latent reservoir in the brain for SIV animal studies. After this latent SIV reservoir was estimated, the effect of latency reversing agents in the brain was evaluated and the mathematical model indicated that there exists a biologically realistic parameter regime where the “Shock and Kill” therapy strategy is safe and effective in the brain. This study is described in Chapter 4 and Chapter 5. The fourth study in this thesis is about estimating and predicting HIV-1 infection in the plasma for HIV-1 Elite Controllers and a comparison group of HIV-1 patients from the Northern Alberta HIV Program. This was the first mathematical modeling study to directly estimate the differences between a group of HIV-1 Elite Controllers with a comparison group of HIV-1 patients using empiric data and it is also the first HIV-1 mathematical model to consider both effector cytotoxic CD4 T lymphocytes' and effector cytotoxic CD8 T lymphocytes' impact on HIV-1 disease and other diseases present in each patient. The response function used for the HIV-1 specific effector cytotoxic T lymphocytes has a biological interpretation based on the phases of antiviral cytotoxic T lymphocyte response and it was found that this response function was important for explaining the observed viral load behavior for the HIV-1 patients in this study. The Elite Controller group was found to have a stronger antiviral immune response than the comparison group. In contrast, the comparison group was found to have more chronic immune activation but a less effective immune response. The Elite Controller immune response estimates given in this study quantifies a biologically realistic optimal immune response goal for HIV-1 therapeutic initiatives. This study is presented in Chapter 6 and Chapter 7.