Random time-shift approximation enables hierarchical Bayesian inference of mechanistic within-host viral dynamics models on large datasets

Mechanistic mathematical models of within-host viral dynamics are tools for understanding how a virus’ biology and its interaction with the immune system shape the infectivity of a host. The biology of the process is encoded by the structure and parameters of the model that can be inferred statistically by fitting to viral load data. The main drawback of mechanistic models is that this inference is computationally expensive because the model must be repeatedly solved. This limits the size of the datasets that can be considered or the complexity of the models fitted. In this paper we develop a much cheaper inference method for this class of models by implementing a novel approximation of the model dynamics that uses a combination of random and deterministic processes. This approximation also properly accounts for process noise early in the infection when cell and virion numbers are small, which is important for the viral dynamics but often overlooked. Our method runs on a consumer laptop and is fast enough to facilitate a full hierarchical Bayesian treatment of the problem with sharing of information to allow for individual level parameter differences. We apply our method to simulated datasets and a reanalysis of COVID-19 monitoring data in an National Basketball Association cohort of 163 individuals.Author summary: Understanding how viruses reproduce within an infected host is crucial for predicting disease progression and evaluating treatments. One way to study this is by using mathematical models that describe how viruses reproduce in the body, such as in the respiratory tract. These models help understand key biological processes, but they require significant computing power, making it difficult to analyse data from large groups of individuals. In this study we developed a new, faster, method for analysing viral load data. Our approach combines randomness, to account for chance events early in infection, with a more predictable model once the infection is well established. This allows us to speed up calculations while capturing key biological processes and maintaining a high degree of accuracy. Our method is efficient enough to run on a laptop, making it possible to study large datasets using a full statistical approach that accounts for individual differences. We tested our method on 200 simulated datasets and applied it to real-world data from 163 individuals in a COVID-19 monitoring study. Our results show that the model can accurately estimate key parameters and track viral load dynamics over time.