Analysis of a stochastic SICR epidemic model associated with the Lévy jump
Date
2022
Authors
Srivastava, H.M.
Danane, Jaouad
Journal Title
Journal ISSN
Volume Title
Publisher
Applied Sciences
Abstract
We propose and study a Susceptible-Infected-Confined-Recovered (SICR) epidemic model.
For the proposed model, the driving forces include (for example) the Brownian motion processes
and the jump Lévy noise. Usually, in the existing literature involving epidemiology models, the
Lévy noise perturbations are ignored. However, in view of the presence of strong fluctuations in the
SICR dynamics, it is worth including these perturbations in SICR epidemic models. Quite frequently,
this results in several discontinuities in the processes under investigation. In our present study,
we consider our SICR model after justifying its used form, namely, the component related to the
Lévy noise. The existence and uniqueness of a global positive solution is established. Under some
assumptions, we show the extinction and the persistence of the infection. In order to give some
numerical simulations, we illustrate a new numerical method to validate our theoretical findings.
Description
Keywords
Susceptible-Infected-Confined-Recovered (SICR) epidemic model, Lévy jump, stochastic model, Brownian motion, extinction, persistence
Citation
Srivastava, H. M. & Danane, J. (2022). “Analysis of a stochastic SICR epidemic model associated with the Lévy jump.” Applied Sciences, 12(17), 8434. https://doi.org/10.3390/app12178434