A Stochastic Kinetic Type Reactions Model for COVID-19

Giorgio Sonnino, Fernando Mora and Pasquale Nardone
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Giorgio Sonnino: Faculté de Sciences, Campus de la Plaine CP 231, Université Libre de Bruxelles (ULB), Bvd du Triomphe, 1050 Brussels, Belgium
Fernando Mora: Institut de Physique de Nice, CNRS, Parc Valrose, Université Côte d’Azur, 06108 Nice, France
Pasquale Nardone: Faculté de Sciences, Campus de la Plaine CP 231, Université Libre de Bruxelles (ULB), Bvd du Triomphe, 1050 Brussels, Belgium

Mathematics, 2021, vol. 9, issue 11, 1-35

Abstract: We propose two stochastic models for the Coronavirus pandemic. The statistical properties of the models, in particular the correlation functions and the probability density functions, were duly computed. Our models take into account the adoption of lockdown measures as well as the crucial role of hospitals and health care institutes. To accomplish this work we adopt a kinetic-type reaction approach where the modelling of the lockdown measures is obtained by introducing a new mathematical basis and the intensity of the stochastic noise is derived by statistical mechanics. We analysed two scenarios: the stochastic S I S -model (Susceptible ? Infectious ? Susceptible) and the stochastic S I S -model integrated with the action of the hospitals; both models take into account the lockdown measures. We show that, for the case of the stochastic SIS-model, once the lockdown measures are removed, the Coronavirus infection will start growing again. However, the combined contributions of lockdown measures with the action of hospitals and health institutes is able to contain and even to dampen the spread of the SARS-CoV-2 epidemic. This result may be used during a period of time when the massive distribution of vaccines in a given population is not yet feasible. We analysed data for USA and France. In the case of USA, we analysed the following situations: USA is subjected to the first wave of infection by Coronavirus and USA is in the second wave of SARS-CoV-2 infection. The agreement between theoretical predictions and real data confirms the validity of our approach.

Keywords: COVID-19; dynamics of population; mathematical modelling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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