Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics
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Abstract
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.
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SciScore for 10.1101/2021.09.30.21264339: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Ethics not detected. Sex as a biological variable not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:However, limitation of current vaccination models lies in either neglecting memory effects or compensating by highly dimensional models with dozens of ordinary differential equations. In this study, we used partial differential equations to develop a model …
SciScore for 10.1101/2021.09.30.21264339: (What is this?)
Please note, not all rigor criteria are appropriate for all manuscripts.
Table 1: Rigor
Ethics not detected. Sex as a biological variable not detected. Randomization not detected. Blinding not detected. Power Analysis not detected. Table 2: Resources
No key resources detected.
Results from OddPub: We did not detect open data. We also did not detect open code. Researchers are encouraged to share open data when possible (see Nature blog).
Results from LimitationRecognizer: We detected the following sentences addressing limitations in the study:However, limitation of current vaccination models lies in either neglecting memory effects or compensating by highly dimensional models with dozens of ordinary differential equations. In this study, we used partial differential equations to develop a model than can capture medium and long term hospital admission dynamics in a population with natural and vaccine-induced immunity only with 8 general compartments. Regarding the sensitivity analysis, the contact matrix unexpectedly contributed more variance in daily hospital admissions than the VOC related increase of virulence itself. This predominant role is somehow surprising because although there are transmission and sensitivity differences based on age (e.g. [Davies, Klepac, et al., 2020]), the strongest age differences appear in the IFR. And more precisely, contact to younger age groups appeared to be the most important contributor to outcome variance, although they were, and by far, the less likely to be hospitalized. An important limitation of the model is that the contact matrix is assumed not to vary over the course of a simulated epidemic. As suggested by the temporal variance in the SPF matrix data (Figure 2), this may be oversimplistic. For instance, we observed a difference of patterns in simulations whether they assumed an high or low contact rates among younger age-classes (as shown on Supplementary Figure S4). A baseline for the different contacts rates, if such a concept can even exist biologically, would most ...
Results from TrialIdentifier: No clinical trial numbers were referenced.
Results from Barzooka: We did not find any issues relating to the usage of bar graphs.
Results from JetFighter: We did not find any issues relating to colormaps.
Results from rtransparent:- Thank you for including a conflict of interest statement. Authors are encouraged to include this statement when submitting to a journal.
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- No protocol registration statement was detected.
Results from scite Reference Check: We found no unreliable references.
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