Math. Model. Nat. Phenom.
Volume 17, 2022
Mathematical Models and Methods in Epidemiology
|Number of page(s)
|29 March 2022
Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics
MIVEGEC, Univ. Montpellier, CNRS, IRDw,
2 Swiss Tropical and Public Health Institute (Swiss TPH), 4002 Basel, Switzerland.
3 Center for Interdisciplinary Research in Biology (CIRB), College de France, CNRS, INSERM, Université PSL, Paris, France.
* Corresponding author: email@example.com
Accepted: 26 February 2022
The Covid-19 pandemic outbreak was followed by a huge amount of modelling studies in order to rapidly gain insights to implement the best public health policies. Most of these compartmental models involved ordinary differential equations (ODEs) systems. Such a formalism implicitly assumes that the time spent in each compartment does not depend on the time already spent in it, which is at odds with the clinical data. To overcome this “memoryless” issue, a widely used solution is to increase and chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity and thus be closer to the observed situation, but also tends to make the whole model more difficult to apprehend and parameterize. We develop a non-Markovian alternative formalism based on partial differential equations (PDEs) instead of ODEs, which, by construction, provides a memory structure for each compartment thereby allowing us to limit the number of compartments. We apply our model to the French 2021 SARS-CoV-2 epidemic and, while accounting for vaccine-induced and natural immunity, we analyse and determine the major components that contributed to the Covid-19 hospital admissions. The results indicate that the observed vaccination rate alone is not enough to control the epidemic, and a global sensitivity analysis highlights a huge uncertainty attributable to the age-structured contact matrix. Our study shows the flexibility and robustness of PDE formalism to capture national COVID-19 dynamics and opens perspectives to study medium or long-term scenarios involving immune waning or virus evolution.
Mathematics Subject Classification: 92D30
Key words: Epidemiology / infectious diseases modelling / contact matrix / partial differential equations / Covid-19
Editor's note: A previous version of this article was reviewed and recommended by Peer Community in Mathematical and Computational Biology: Bastien Reyné, Quentin Richard, Camille Noûs, Christian Selinger, Mircea T. Sofonea, Ramsès Djidjou-Demasse, Samuel Alizon (2022). Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics. Peer Community in Mathematical and Computational Biology, https://doi.org/10.24072/pci.mcb.100008.
© The authors. Published by EDP Sciences, 2022
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