COVID-19 spread around the globe in early 2020 and has deeply changed our everyday life [1]. Mathematical models allow us to estimate R0 (basic reproduction number), understand the progression of viral infection, explore the impacts of quarantine on the epidemic, and most importantly, predict the future outbreak [2]. The most classical model is SIR, which describes time evolution of three variables, i.e., number of susceptible people (S), number of people infected (I), and number of people who have recovered (R), based on their transition rates [3]. Despite the simplicity, SIR model produces several general predictions that have important implications for public health [3].

SIR model includes three populations with distinct labels and is thus compartmentalized. Extra compartments can be added to describe additional states of populations, for example, people exposed to the virus but not yet infectious. However, a model with more compartments, though more realistic, is also more difficult to parameterize and analyze. The study by Reyné et al. [4] proposed an alternative formalism based on PDE (partial differential equation), which allows modeling different biological scenarios without the need of adding additional compartments. As illustrated, the authors modeled hospital admission dynamics in a vaccinated population only with 8 general compartments.

The main conclusion of this study is that the vaccination level till 2021 summer was insufficient to prevent a new epidemic in France. Additionally, the authors used alternative data sources to estimate the age-structured contact patterns. By sensitivity analysis on a daily basis, they found that the 9 parameters in the age-structured contact matrix are most variable and thus shape Covid19 pandemic dynamics. This result highlights the importance of incorporating age structure of the host population in modeling infectious diseases. However, a relevant potential limitation is that the contact matrix was assumed to be constant throughout the simulations. To account for time dependence of the contact matrix, social and behavioral factors need to be integrated [5].

References

[1] Hu B, Guo H, Zhou P, Shi Z-L (2021) Characteristics of SARS-CoV-2 and COVID-19. Nature Reviews Microbiology, 19, 141–154. https://doi.org/10.1038/s41579-020-00459-7

[2] Jinxing G, Yongyue W, Yang Z, Feng C (2020) Modeling the transmission dynamics of COVID-19 epidemic: a systematic review. The Journal of Biomedical Research, 34, 422–430. https://doi.org/10.7555/JBR.34.20200119

[3] Tolles J, Luong T (2020) Modeling Epidemics With Compartmental Models. JAMA, 323, 2515–2516. https://doi.org/10.1001/jama.2020.8420

[4] Reyné B, Richard Q, Noûs C, Selinger C, Sofonea MT, Djidjou-Demasse R, Alizon S (2022) Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics. medRxiv, 2021.09.30.21264339, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.09.30.21264339

[5] Bedson J, Skrip LA, Pedi D, Abramowitz S, Carter S, Jalloh MF, Funk S, Gobat N, Giles-Vernick T, Chowell G, de Almeida JR, Elessawi R, Scarpino SV, Hammond RA, Briand S, Epstein JM, Hébert-Dufresne L, Althouse BM (2021) A review and agenda for integrated disease models including social and behavioural factors. Nature Human Behaviour, 5, 834–846 https://doi.org/10.1038/s41562-021-01136-2