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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Nature Portfolio
2021-07-01
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| Series: | Scientific Reports |
| Online Access: | https://doi.org/10.1038/s41598-021-93388-1 |
| _version_ | 1818346979953999872 |
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| author | Roberto Beneduci Eleonora Bilotta Pietro Pantano |
| author_facet | Roberto Beneduci Eleonora Bilotta Pietro Pantano |
| author_sort | Roberto Beneduci |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-13T17:26:53Z |
| format | Article |
| id | doaj.art-682b66f206d345bcb3cd0d0ad2e3d951 |
| institution | Directory Open Access Journal |
| issn | 2045-2322 |
| language | English |
| last_indexed | 2024-12-13T17:26:53Z |
| publishDate | 2021-07-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj.art-682b66f206d345bcb3cd0d0ad2e3d9512022-12-21T23:37:10ZengNature PortfolioScientific Reports2045-23222021-07-0111111110.1038/s41598-021-93388-1A unifying nonlinear probabilistic epidemic model in space and timeRoberto Beneduci0Eleonora Bilotta1Pietro Pantano2Department of Physics, University of CalabriaDepartment of Physics, University of CalabriaDepartment of Physics, University of CalabriaAbstract 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.https://doi.org/10.1038/s41598-021-93388-1 |
| spellingShingle | Roberto Beneduci Eleonora Bilotta Pietro Pantano A unifying nonlinear probabilistic epidemic model in space and time Scientific Reports |
| title | 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_short | A unifying nonlinear probabilistic epidemic model in space and time |
| title_sort | unifying nonlinear probabilistic epidemic model in space and time |
| url | https://doi.org/10.1038/s41598-021-93388-1 |
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