Mathematical models of viral latency

•We review mathematical models of proviral latency relevant for HIV treatment design.•We review epidemiological aspects of episomal latency and address limitations of those models.•We suggest an extension of known mathematical models by delay differential equations.•Finally, we discuss the challenges of data integration for clinical decision support.

While viral latency remains one of the biggest challenges for successful antiviral therapy, it has also inspired mathematical modelers to develop dynamical system approaches with the aim of predicting the impact of drug efficacy on disease progression and the persistence of latent viral reservoirs. In this review we present several differential equation models and assess their relative success in giving advice to the working clinician and their predictive power for inferring long term viral eradication from short term abatement. Many models predict that there is a considerable likelihood of viral rebound due to continuous reseeding of latent reservoirs. Most mathematical models of HIV latency suffer from being reductionist by ignoring the growing variety of different cell types harboring latent virus, the considerable intercellular delay involved in reactivation, and host-related epigenetic modifications which may alter considerably the dynamical system of immune cell populations.