Exploring the effect of density dependent infection rate in a within host viral infection model

The most common viral dynamics models for analyzing viral infections assume a well-mixed spatial distribution between viral particles and uninfected target cells. However, throughout an infection, the spatial distribution of virus and cells changes. Initially, virus and infected cells are localized so that a target cell in an area with lower virus presence will be less likely to be infected than a cell close to a location of viral production. A density-dependent infection rate has the potential to improve models that treat the cellular infection probability as a constant. Building on previous work that used epidemiological models, which introduced Saturated Incidence, Beddington-DeAngelis, and Crowley Martin models to simulate spatial heterogeneity in population-level models, we implemented these density-dependent models in within-host viral kinetics models to understand how a density dependent infection rate might impact the predicted severity of an influenza infection. The parameter values that govern the strength of density dependence were varied to understand the implications of density dependent infection rate on disease severity and the potential impacts on patient treatment. For low density dependence, a steeper increase in the virus and a higher viral peak was predicted. We find that the initial localization of infected cells slows the progression of the infection, thus suggesting that accounting for density dependence when analyzing influenza infection severity can result in an altered expectation for viral progression.