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In-host models have been essential for understanding the dynamics of virus infection inside an infected individual. When used together with biological data, they provide insight into viral life cycle, intracellular and cellular virus–host interactions, and the role, efficacy, and mode of action of therapeutics. In this review, we present the standard model of virus dynamics and highlight situations where added model complexity accounting for intracellular processes is needed. We present several examples from acute and chronic viral infections where such inclusion in explicit and implicit manner has led to improvement in parameter estimates, unification of conclusions, guidance for targeted therapeutics, and crossover among model systems. We also discuss trade-offs between model realism and predictive power and highlight the need of increased data collection at finer scale of resolution to better validate complex models. 

The antiviral remdesivir has been approved by regulatory bodies such as the European Medicines Agency (EMA) and the US Food and Drug administration (FDA) for the treatment of COVID-19. However, its efficacy is debated and toxicity concerns might limit the therapeutic range of this drug. Computational models that aid in balancing efficacy and toxicity would be of great help. Parametrizing models is difficult because the prodrug remdesivir is metabolized to its active form (RDV-TP) upon cell entry, which complicates dose–activity relationships. Here, we employ a computational model that allows drug efficacy predictions based on the binding affinity of RDV-TP for its target polymerase in SARS-CoV-2. We identify an optimal infusion rate to maximize remdesivir efficacy. We also assess drug efficacy in suppressing both wild-type and resistant strains, and thereby describe a drug regimen that may select for resistance. Our results differ from predictions using prodrug dose–response curves (pseudo-EC50s). We expect that reaching 90% inhibition (EC90) is insufficient to suppress SARS-CoV-2 in the lungs. While standard dosing mildly inhibits viral polymerase and therefore likely reduces morbidity, we also expect selection for resistant mutants for most realistic parameter ranges. To increase efficacy and safeguard against resistance, we recommend more clinical trials with dosing regimens that substantially increase the levels of RDV-TP and/or pair remdesivir with companion antivirals. 

Antiretroviral therapy (ART) effectively controls HIV infection, suppressing HIV viral loads. Typically suspension of therapy is rapidly followed by rebound of viral loads to high, pre-therapy levels. Indeed, a recent study showed that approximately 90% of treatment interruption study participants show viral rebound within at most a few months of therapy suspension, but the remaining 10%, showed viral rebound some months, or years, after ART suspension. Some may even never rebound. We investigate and compare branching process models aimed at gaining insight into these viral dynamics. Specifically, we provide a theory that explains both short- and long-term viral rebounds, and post-treatment control, via a multitype branching process with time-inhomogeneous rates, validated with data from Li et al. (Li et al. 2016 AIDS 30 , 343–353. ( doi:10.1097/QAD.0000000000000953 )). We discuss the associated biological interpretation and implications of our best-fit model. To test the effectiveness of an experimental intervention in delaying or preventing rebound, the standard practice is to suspend therapy and monitor the study participants for rebound. We close with a discussion of an important application of our modelling in the design of such clinical trials.