Quantitative viral dynamics: Methods for parameter estimation

Fitting mathematical models of viral dynamics to serial, quantitative viral load data provides inferences on the mechanisms in virus infection. This process can reveal the speed and magnitude of viral replication, cell proliferation and death, immune responses, and/or treatment efficacy. Viral dynamics modeling involves developing conceptual models, translating them into equations, and applying the appropriate statistical tools to determine the optimal parameters such that the model recapitulates observations from human and animal infections. In this review, we outline the theoretical foundations needed to understand model fitting, parameter estimation, and what it means to achieve a good fit. We provide examples and explain the strengths and limitations of three commonly used model fitting approaches: individual fitting, population mixed effects fitting, and feature fitting. We briefly review fitting algorithms and highlight powerful available computer software packages that can be used for fitting and parameter estimation. We discuss different model types, parameter identifiability, and how future modeling efforts can leverage advances in multi-dimensional data. Finally, we conclude with simple guidelines for choosing the best approach based on available data and scientific questions.