Skip to main page content
U.S. flag

An official website of the United States government

Dot gov

The .gov means it’s official.
Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you’re on a federal government site.

Https

The site is secure.
The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Access keys NCBI Homepage MyNCBI Homepage Main Content Main Navigation
Editorial
. 2022 Feb;41(1):101017.
doi: 10.1016/j.accpm.2021.101017. Epub 2021 Dec 28.

Principles of mathematical epidemiology and compartmental modelling application to COVID-19

Bastien Reyné  1 , Nicolas Saby  2 , Mircea T Sofonea  3
Affiliations
Editorial

Principles of mathematical epidemiology and compartmental modelling application to COVID-19

Bastien Reyné et al. Anaesth Crit Care Pain Med. 2022 Feb.
No abstract available

Keywords: Basic reproduction number; Epidemiology; Hospital dynamics; Infectious diseases modelling; Ordinary differential equations.

PubMed Disclaimer

Figures

Fig. 1
Fig. 1
Illustrative compartmental model to estimate hospital occupancy. Susceptible individuals (Scompartment) become infected after being in contact with infected individuals. They can develop an asymptomatic or mild version of the disease (I) before recovering (R), or they can become severely infected (Is). In the latter, they will transmit the disease as the other infected individuals then end up in the hospital (H) before recovery or death (D).
Fig. 2
Fig. 2
The probability for a given individual of remaining in a specific compartment in a classical and simple SIR model, like the infected compartment (I) in Model 1 follows an exponential distribution which is memoryless – meaning the time spent in the compartment does not depend on the time already spent in the compartment, which is unrealistic. A workaround consists of chaining compartments as I1 and I2 in Model 2, thus creating some heterogeneity and adding memory. For instance, to specify that an individual who just entered a compartment has a very low probability to clear the disease instantly, and on the contrary if she/he spent already some significant time infected, she/he has a higher probability to clear the disease.
Fig. 3
Fig. 3
The model used by Ref. to estimate the hospital conventional beds occupancy and ICU beds occupancy. In this model, individuals can be either susceptible (S), exposed (E), infected but not hospitalised (I), hospitalised in conventional beds (H), hospitalised in ICU (ICU) or removed (R/D).
See this image and copyright information in PMC

Similar articles

See all similar articles

Cited by

References

    1. Adam D. Special report: the simulations driving the world’s response to COVID-19. Nature. 2020;580(7803):316–318. doi: 10.1038/d41586-020-01003-6. - DOI - PubMed
    1. Siegenfeld A.F., Taleb N.N., Bar-Yam Y. Opinion: what models can and cannot tell us about COVID-19. Proc Natl Acad Sci. 2020;117(28):16092–16095. doi: 10.1073/pnas.2011542117. - DOI - PMC - PubMed
    1. Keeling M.J., Rohani P. Princeton University Press; 2008. Modeling infectious diseases in humans and animals. - DOI
    1. Kermack W.O., McKendrick A.G. A contribution to the mathematical theory of epidemics. Proc R Soc Lond Ser Contai Pap Math Phys Character. 1927;115(772):700–721. doi: 10.1098/rspa.1927.0118. - DOI
    1. Sofonea M.T., Reyné B., Elie B., Djidjou-Demasse R., Selinger C., Michalakis Y., et al. Memory is key in capturing COVID-19 epidemiological dynamics. Epidemics. 2021;35 doi: 10.1016/j.epidem.2021.100459. - DOI - PMC - PubMed

Publication types