Non-Markovian modelling highlights the importance of age structure on Covid-19 epidemiological dynamics

Abstract

The Covid-19 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 unrealistic. To overcome this “memoryless” issue, a widely used solution is to chain the number of compartments of a unique reality (e.g. have infected individual move between several compartments). This allows for greater heterogeneity, 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. We apply our model to the French 2021 SARS-CoV-2 epidemic and we determine the major components that contributed to the Covid-19 hospital admissions. 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.