The number of daily new cases of an epidemic is assumed to evolve as the exponential of a Wiener process with Poissonian jumps that are exponentially distributed. The model parameters can be estimated by using the method of moments. In an application to the COVID-19 pandemic in the province of Québec, Canada, the proposed model is shown to be acceptable. General formulas for the probability that a given increase in the number of daily new cases is due to the normal variations of the continuous part of the process or rather to a jump of this process are given. Based on these formulas, the probability of observing the likely start of a new wave of infections is calculated for the application to the COVID-19 pandemic.
Citation: Mario Lefebvre. A Wiener process with jumps to model the logarithm of new epidemic cases[J]. AIMS Biophysics, 2022, 9(3): 271-281. doi: 10.3934/biophy.2022023
The number of daily new cases of an epidemic is assumed to evolve as the exponential of a Wiener process with Poissonian jumps that are exponentially distributed. The model parameters can be estimated by using the method of moments. In an application to the COVID-19 pandemic in the province of Québec, Canada, the proposed model is shown to be acceptable. General formulas for the probability that a given increase in the number of daily new cases is due to the normal variations of the continuous part of the process or rather to a jump of this process are given. Based on these formulas, the probability of observing the likely start of a new wave of infections is calculated for the application to the COVID-19 pandemic.
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Mario Lefebvre. A Wiener process with jumps to model the logarithm of new epidemic cases[J]. AIMS Biophysics, 2022, 9(3): 271-281. doi: 10.3934/biophy.2022023
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