Continuous-time stochastic processes for the spread of COVID-19 disease simulated via a Monte Carlo approach and comparison with deterministic models

Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S , infected I , removed R and dead people D . In order to have a cross validation, a deterministic version of such a model is a...

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Bibliographic Details
Published in:Journal of mathematical biology 2021-10, Vol.83 (4), p.34-34, Article 34
Main Authors: Calleri, Fabiana, Nastasi, Giovanni, Romano, Vittorio
Format: Article
Language:English
Subjects:
Applications of Mathematics
Compartments
Coronaviruses
COVID-19
Differential equations
Disease control
Herd immunity
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Ordinary differential equations
Pandemics
Stochastic models
Stochastic processes
Viral diseases
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Summary:Two stochastic models are proposed to describe the evolution of the COVID-19 pandemic. In the first model the population is partitioned into four compartments: susceptible S , infected I , removed R and dead people D . In order to have a cross validation, a deterministic version of such a model is also devised which is represented by a system of ordinary differential equations with delays. In the second stochastic model two further compartments are added: the class A of asymptomatic individuals and the class L of isolated infected people. Effects such as social distancing measures are easily included and the consequences are analyzed. Numerical solutions are obtained with Monte Carlo simulations. Quantitative predictions are provided which can be useful for the evaluation of political measures, e.g. the obtained results suggest that strategies based on herd immunity are too risky. Finally, the models are calibrated on data referring to the second wave of infection in Italy.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-021-01657-4