Within the human respiratory tract (HRT), viruses diffuse through the periciliary fluid (PCF) bathing the epithelium, and travel upwards via advection towards the nose and mouth, as the mucus escalator entrains the PCF. While many mathematical models (MMs) to date have described the course of influenza A virus (IAV) infections in vivo, none have considered the impact of both diffusion and advection on the kinetics and localization of the infection. The MM herein represents the HRT as a one-dimensional track extending from the nose down to a depth of 30 cm, wherein stationary cells interact with the concentration of IAV which move along within the PCF. When IAV advection and diffusion are both considered, the former is found to dominate infection kinetics, and a 10-fold increase in the virus production rate is required to counter its effects. The MM predicts that advection prevents infection from disseminating below the depth at which virus first deposits. Because virus is entrained upwards, the upper HRT sees the most virus, whereas the lower HRT sees far less. As such, infection peaks and resolves faster in the upper than in the lower HRT, making it appear as though infection progresses from the upper towards the lower HRT. When the spatial MM is expanded to include cellular regeneration and an immune response, it can capture the time course of infection with a seasonal and an avian IAV strain by shifting parameters in a manner consistent with what is expected to differ between these two types of infection. The impact of antiviral therapy with neuraminidase inhibitors was also investigated. This new MM offers a convenient and unique platform from which to study the localization and spread of respiratory viral infections within the HRT.
The endpoint dilution assay’s output, the 50% infectious dose (ID50), is calculated using the Reed-Muench or Spearman-Kärber mathematical approximations, which are biased and often miscalculated. We introduce a replacement for the ID50 that we call Specific INfection (SIN) along with a free and open-source web-application, midSIN (https://midsin.physics.ryerson.ca) to calculate it. midSIN computes a virus sample’s SIN concentration using Bayesian inference based on the results of a standard endpoint dilution assay, and requires no changes to current experimental protocols. We analyzed influenza and respiratory syncytial virus samples using midSIN and demonstrated that the SIN/mL reliably corresponds to the number of infections a sample will cause per mL. It can therefore be used directly to achieve a desired multiplicity of infection, similarly to how plaque or focus forming units (PFU, FFU) are used. midSIN’s estimates are shown to be more accurate and robust than the Reed-Muench and Spearman-Kärber approximations. The impact of endpoint dilution plate design choices (dilution factor, replicates per dilution) on measurement accuracy is also explored. The simplicity of SIN as a measure and the greater accuracy provided by midSIN make them an easy and superior replacement for the TCID50 and other in vitro culture ID50 measures. We hope to see their universal adoption to measure the infectivity of virus samples.
In Fig 3 there is an error in the text in the legend within the figure for parts d, e, f. It says 1 dpi, 2 dpi, 3 dpi, 4 dpi, 7 dpi, 7 dpi, but it should say 0 dpi, 1 dpi, 2 dpi, 3 dpi, 4 dpi, 7 dpi. The authors have provided a corrected version here.
In Fig 7 there is an error in the figure caption. The correct figure caption is provided below. Fig 7. The effect of cellular regeneration on the MM prediction of IAV infection kinetics. The effect of varying (a-c) the regeneration rate (r D ) or (d-f) the regeneration delay (τ D ) are shown. Unless varied, τ D = 1 d and r D = 0.75 d -1 .
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