Article ; Online: A unifying nonlinear probabilistic epidemic model in space and time.
2021 Volume 11, Issue 1, Page(s) 13860
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 ... ...
| 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. |
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| MeSH term(s) | Algorithms ; COVID-19/epidemiology ; Computer Simulation ; Humans ; Models, Biological ; Models, Statistical ; Models, Theoretical ; SARS-CoV-2/pathogenicity ; Stochastic Processes |
| Language | English |
| Publishing date | 2021-07-05 |
| Publishing country | England |
| Document type | Journal Article |
| ZDB-ID | 2615211-3 |
| ISSN | 2045-2322 ; 2045-2322 |
| ISSN (online) | 2045-2322 |
| ISSN | 2045-2322 |
| DOI | 10.1038/s41598-021-93388-1 |
| Database | MEDical Literature Analysis and Retrieval System OnLINE |
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