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Interactions between SARS-CoV-2 and the immune system during infection are complex. However, understanding the within-host SARS-CoV-2 dynamics is of enormous importance for clinical and public health outcomes. Current mathematical models focus on describing the within-host SARS-CoV-2 dynamics during the acute infection phase. Thereby they ignore important long-term post-acute infection effects. We present a mathematical model, which not only describes the SARS-CoV-2 infection dynamics during the acute infection phase, but extends current approaches by also recapitulating clinically observed long-term post-acute infection effects, such as the recovery of the number of susceptible epithelial cells to an initial pre-infection homeostatic level, a permanent and full clearance of the infection within the individual, immune waning, and the formation of long-term immune capacity levels after infection. Finally, we used our model and its description of the long-term post-acute infection dynamics to explore reinfection scenarios differentiating between distinct variant-specific properties of the reinfecting virus. Together, the model's ability to describe not only the acute but also the long-term post-acute infection dynamics provides a more realistic description of key outcomes and allows for its application in clinical and public health scenarios. • A novel model of the within-host SARS-CoV-2 infection dynamics. • Describes acute infection dynamics of individual viral load data accurately. • Reveals long-term post-acute SARS-CoV-2 infection dynamics. • Accommodates reinfections accounting for higher infectivity or immune escape variants. [ABSTRACT FROM AUTHOR]

Highlights: [•] We study hepatitis C virus dynamics using a multiscale age-structured model. [•] The model includes intracellular RNA replication and extracellular viral infection. [•] Stability analysis of the steady states is performed. [•] Approximations of the viral decline are derived and compared with the full model. [•] We discuss other ways to incorporate intracellular viral dynamics into the model. [Copyright &y& Elsevier]

In Wick and Stelf [Math. Biosci. 187 (2004) 1], we showed how to simulate a pair of strongly interacting biological populations evolving stochastically over many orders-of-magnitude. Here we generalize the method to any (finite) number of compartments; transitions including births, deaths, progression through life-stages, and mitoses; and arbitrary rate functions. We illustrate the technique for a seven-compartment model of the cellular immune response to a viral infection. [Copyright &y& Elsevier]

Cites a study by researchers in the U.S., which asserted that mathematical modeling of viral decay may be a useful method to evaluate single or combination therapy for hepatitis B virus (HBV) infection. Use of mathematical modeling of viral decay kinetics to rapidly assess potential antiviral regimens; Examination of the kinetics of viral replication in chronic HB patients randomized to lamivudine 100 mg vs. 600 mg; Manifestation by patients receiving 600mg daily lamivudine of a faster decay rate in the infected cell compartment.