Modelling, analysis, observability and identifiability of epidemic dynamics with reinfections
05/05/2022 Thursday 5th May 2022, 16:00 (Room P3.10, Mathematics Building)
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PierreAlexandre Bliman, INRIA, Sorbonne Université, Université ParisDiderot SPC, CNRS, Laboratoire JacquesLouis Lions, Paris, France
In order to understand if counting the number of reinfections may provide supplementary information on the evolution of an epidemic, we consider in this paper a general SEIRS model describing the dynamics of an infectious disease including latency, waning immunity and infectioninduced mortality. We derive an infinite system of differential equations that provides an image of the same infection process, but counting also the reinfections. Wellposedness is established in a suitable space of sequence valued functions, and the asymptotic behavior of the solutions is characterized, according to the value of the basic reproduction number. This allows to determine several mean numbers of reinfections related to the population at endemic equilibrium. We then show how using jointly measurement of the number of infected individuals and of the number of primoinfected provides observability and identifiability to a simple SIS model for which none of these two measures is sufficient to ensure on its own the same properties. This is a joint work with Marcel Fang. More details may be found in the report https://arxiv.org/abs/2011.12202.
