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.

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 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.
Scheda breve Scheda completa Scheda completa (DC)
2021
COVID-19
Computer Simulation
Humans
Models, Biological
Models, Theoretical
SARS-CoV-2
Stochastic Processes
Algorithms
Models, Statistical
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/20.500.11770/327353`
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