A unifying nonlinear probabilistic epidemic model in space and time

Abstract Covid-19 epidemic dramatically relaunched the importance of mathematical modelling in supporting governments decisions to slow down the disease propagation. On the other hand, it remains a challenging task for mathematical modelling. The interplay between different models could be a key ele...

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Autores principales:	Roberto Beneduci, Eleonora Bilotta, Pietro Pantano
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2021
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/682b66f206d345bcb3cd0d0ad2e3d951
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spelling	oai:doaj.org-article:682b66f206d345bcb3cd0d0ad2e3d9512021-12-02T15:39:50ZA unifying nonlinear probabilistic epidemic model in space and time10.1038/s41598-021-93388-12045-2322https://doaj.org/article/682b66f206d345bcb3cd0d0ad2e3d9512021-07-01T00:00:00Zhttps://doi.org/10.1038/s41598-021-93388-1https://doaj.org/toc/2045-2322Abstract Covid-19 epidemic dramatically relaunched the importance of mathematical modelling in supporting governments decisions to slow down the disease propagation. On the other hand, it remains a challenging task for mathematical modelling. The interplay between different models could be a key element in the modelling strategies. Here we propose a continuous space-time non-linear probabilistic model from which we can derive many of the existing models both deterministic and stochastic as for example SI, SIR, SIR stochastic, continuous-time stochastic models, discrete stochastic models, Fisher–Kolmogorov model. A partial analogy with the statistical interpretation of quantum mechanics provides an interpretation of the model. Epidemic forecasting is one of its possible applications; in principle, the model can be used in order to locate those regions of space where the infection probability is going to increase. The connection between non-linear probabilistic and non-linear deterministic models is analyzed. In particular, it is shown that the Fisher–Kolmogorov equation is connected to linear probabilistic models. On the other hand, a generalized version of the Fisher–Kolmogorov equation is derived from the non-linear probabilistic model and is shown to be characterized by a non-homogeneous time-dependent diffusion coefficient (anomalous diffusion) which encodes information about the non-linearity of the probabilistic model.Roberto BeneduciEleonora BilottaPietro PantanoNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 11, Iss 1, Pp 1-11 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Roberto Beneduci Eleonora Bilotta Pietro Pantano A unifying nonlinear probabilistic epidemic model in space and time
description	Abstract Covid-19 epidemic dramatically relaunched the importance of mathematical modelling in supporting governments decisions to slow down the disease propagation. On the other hand, it remains a challenging task for mathematical modelling. The interplay between different models could be a key element in the modelling strategies. Here we propose a continuous space-time non-linear probabilistic model from which we can derive many of the existing models both deterministic and stochastic as for example SI, SIR, SIR stochastic, continuous-time stochastic models, discrete stochastic models, Fisher–Kolmogorov model. A partial analogy with the statistical interpretation of quantum mechanics provides an interpretation of the model. Epidemic forecasting is one of its possible applications; in principle, the model can be used in order to locate those regions of space where the infection probability is going to increase. The connection between non-linear probabilistic and non-linear deterministic models is analyzed. In particular, it is shown that the Fisher–Kolmogorov equation is connected to linear probabilistic models. On the other hand, a generalized version of the Fisher–Kolmogorov equation is derived from the non-linear probabilistic model and is shown to be characterized by a non-homogeneous time-dependent diffusion coefficient (anomalous diffusion) which encodes information about the non-linearity of the probabilistic model.
format	article
author	Roberto Beneduci Eleonora Bilotta Pietro Pantano
author_facet	Roberto Beneduci Eleonora Bilotta Pietro Pantano
author_sort	Roberto Beneduci
title	A unifying nonlinear probabilistic epidemic model in space and time
title_short	A unifying nonlinear probabilistic epidemic model in space and time
title_full	A unifying nonlinear probabilistic epidemic model in space and time
title_fullStr	A unifying nonlinear probabilistic epidemic model in space and time
title_full_unstemmed	A unifying nonlinear probabilistic epidemic model in space and time
title_sort	unifying nonlinear probabilistic epidemic model in space and time
publisher	Nature Portfolio
publishDate	2021
url	https://doaj.org/article/682b66f206d345bcb3cd0d0ad2e3d951
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A unifying nonlinear probabilistic epidemic model in space and time

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