The treatment of human immunodeficiency virus (HIV-1) infection faces the challenge of drug resistance. The high mutation rate of HIV-1 allows it to develop resistance against all available drugs. New mechanisms of intervention that do not succumb to failure through resistance are thus being explored. Mutagens that increase the viral mutation rate are a promising class of drugs. They can drive HIV-1 past a critical mutation rate, called the error threshold, and induce a catastrophic loss of genetic information. The treatment duration for a mutagen to drive HIV-1 beyond this error threshold is not yet estimated. We devise a detailed stochastic simulation of HIV-1 infection to estimate this duration. The simulations predict that the required duration is inversely proportional to the difference between the mutation rate induced by a mutagen and the error threshold. This scaling is robust to changes in simulation parameters. Using this scaling, we estimate the required duration of treatment with mutagens to be many years. Unfortunately, all available drugs, including mutagens, fail to clear the infection because HIV-1 establishes a reservoir of latently infected cells harbouring silent HIV-1 integrated genomes. A new \shock and kill" strategy that aims to activate latent cells and render them susceptible to immune killing or viral cytopathicity and thus to eradicate the HIV-1 latent reservoir has been suggested. Several latency reversal agents (LRAs) have been developed. Individual LRAs fail to show any decline in the HIV-1 latent reservoir in clinical trials. Combinations of LRAs have been tested in a few in-vitro and ex-vivo experiments. It has been found that in combination LRAs act synergistically. Finding the drug concentrations that yield the maximum synergy may be helpful in achieving a sterilizing cure. Here, we develop an intracellular model to estimate these drug concentrations. We choose drugs from two different classes of LRAs and show that our model captures quantitatively recent in-vitro experiments of their activity individually and in combination. With this model, we estimate the concentrations of the drugs required to obtain the maximum synergy. Strong CD8+ T cell responses against viruses have been associated with low levels of viremia. Elite controllers of HIV-1, who are known to have low or undetectable viremia, mount a cross-reactive CD8+ T cell response against the pathogen which controls viral mutation-driven escape from immune activity. These cross-reactive responses are against specific epitopes of HIV-1. Our goal was to examine whether such epitopes could be identified systematically so that a cross-reactive immune response could be induced by using these epitopes as immunogens. Immune recognition of an epitope involves two parts: presentation of the epitope, or peptide, by the major histocompatibility complex (MHC) molecules in the host and high a finity binding of the peptide-MHC complex with a T cell receptor (TCR). Immune escape could occur at either of these steps. Here, we examined the first step. We devise the following procedure to identify peptides that sustain HLA binding despite mutations. First, from the full length HIV-1 (HCV) proteome, we identify viral peptides that bind tightly with MHC molecules using the software NetMHCpan2.8. Next, we pick the peptides and their complementary MHC molecules that yield tight binding and mutate the peptides bit by bit to examine whether binding was compromised. We identify several viral peptide-MHC pairs that display tight binding despite all possible single mutations of the peptides both with HIV-1 and HCV. These peptides present candidates which can be tested for their TCR binding and cross-reactive immunogenic potential.