Nonlinear mixed models and related approaches in infectious disease modeling: A systematic and critical review.

The level of surveillance and preparedness against epidemics varies across countries, resulting in different responses to outbreaks. When conducting an in-depth analysis of microinfection dynamics, one must account for the substantial heterogeneity across countries. However, many commonly used statistical model specifications lack the flexibility needed for sound and accurate analysis and prediction in such contexts. Nonlinear mixed effects models (NLMMs) constitute a specific statistical tool that can overcome these significant challenges. While compartmental models are well-established in infectious disease modeling and have seen significant advancements, Nonlinear Mixed Models (NLMMs) offer a flexible approach for handling heterogeneous and unbalanced repeated measures data, often with less computational effort than some individual-level compartmental modeling techniques. This study provides an overview of their current use and offers a solid foundation for developing guidelines that may help improve their implementation in real-world situations. Relevant scientific databases in the Access initiative programs were used to search for papers dealing with key aspects of NLMMs in infectious disease modeling (IDM). From an initial list of 3641 papers, 124 were finally included and used for this systematic and critical review spanning the last two decades, following the PRISMA guidelines. NLMMs have evolved rapidly in the last decade, especially in IDM, with most publications dating from 2017 to 2021 (83.33%). The routine use of normality assumption appeared inappropriate for IDM, leading to a wealth of literature on NLMMs with non-normal errors and random effects under various estimation methods. We noticed that NLMMs have attracted much attention for the latest known epidemics worldwide (COVID-19, Ebola, Dengue and Lassa) with the robustness and reliability of relaxed propositions of the normality assumption. A case study of the application of COVID-19 data helped to highlight NLMMs' performance in modeling infectious diseases. Out of this study, estimation methods, assumptions, and random terms specification in NLMMs are key aspects requiring particular attention for their application in IDM.