Can the viral reservoir of latently infected CD4(+) T cells be eradicated with antiretroviral HIV drugs?

The majority of cells infected with the human immunodeficiency virus are activated CD4(+) T cells, which can be treated with antiretoviral drugs. However, an obstacle to eradication is the presence of viral reservoirs, such as latently infected CD4(+) T cells. Such cells may be less susceptible to antiretroviral drugs and may persist at low levels during treatment. We introduce a model of impulsive differential equations that describe T cell and drug interactions. We make the extreme assumption that latently infected cells are unaffected by drugs, in order to answer the research question: Can the viral reservoir of latently infected cells be eradicated using current antiretroviral therapy? We analyse the model in both the presence and absence of drugs, showing that, if the frequency of drug taking is sufficiently high, then the number of uninfected CD4(+) T cells approaches the number of T cells in the uninfected immune system. In particular, this implies that the latent reservoir will be eliminated. It follows that, with sufficient application of drugs, latently infected cells cannot sustain a viral reservoir on their own. We illustrate the results with numerical simulations.