@article{fdi:010084615,
  title = {{N}on-{M}arkovian modelling highlights the importance of age structure on {C}ovid-19 epidemiological dynamics},
  author = {{R}eyne, {B}. and {R}ichard, {Q}uentin and {S}elinger, {C}hristian and {S}ofonea, {M}. {T}. and {D}jidjou-{D}emasse, {R}ams{\`e}s and {A}lizon, {S}.},
  editor = {},
  language = {{ENG}},
  abstract = {{T}he {C}ovid-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. {M}ost of these compartmental models involved ordinary differential equations ({ODE}s) systems. {S}uch 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. {T}o 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). {T}his 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. {W}e develop a non-{M}arkovian alternative formalism based on partial differential equations ({PDE}s) instead of {ODE}s, which, by construction, provides a memory structure for each compartment thereby allowing us to limit the number of compartments. {W}e apply our model to the {F}rench 2021 {SARS}-{C}o{V}-2 epidemic and, while accounting for vaccine-induced and natural immunity, we analyse and determine the major components that contributed to the {C}ovid-19 hospital admissions. {T}he 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. {O}ur 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.},
  keywords = {{E}pidemiology ; infectious diseases modelling ; contact matrix ; partial ; differential equations ; {C}ovid-19},
  booktitle = {},
  journal = {{M}athematical {M}odelling of {N}atural {P}henomena},
  volume = {17},
  numero = {},
  pages = {7 [24 ]},
  ISSN = {0973-5348},
  year = {2022},
  DOI = {10.1051/mmnp/2022008},
  URL = {https://www.documentation.ird.fr/hor/fdi:010084615},
}