Solutions of a disease model with fractional white noise

We consider an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations. We generate a new SIRS model and perturb it to the fraction...

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Bibliographic Details
Published in:Chaos, solitons and fractals solitons and fractals, 2020-08, Vol.137, p.109840-109840, Article 109840
Main Authors: Akinlar, M.A., Inc, Mustafa, Gómez-Aguilar, J.F., Boutarfa, B.
Format: Article
Language:English
Subjects:
Euler type numerical method
SIRS model with fractional Brownian motion
Stability analysis
Trapezoidal rule
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Summary:We consider an epidemic disease system by an additive fractional white noise to show that epidemic diseases may be more competently modeled in the fractional-stochastic settings than the ones modeled by deterministic differential equations. We generate a new SIRS model and perturb it to the fractional-stochastic systems. We study chaotic behavior at disease-free and endemic steady-state points on these systems. We also numerically solve the fractional-stochastic systems by an trapezoidal rule and an Euler type numerical method. We also associate the SIRS model with fractional Brownian motion by Wick product and determine numerical and explicit solutions of the resulting system. There is no SIRS-type model which considers fractional epidemic disease models with fractional white noise or Wick product settings which makes the paper totally a new contribution to the related science.
ISSN:0960-0779
1873-2887
0960-0779
DOI:10.1016/j.chaos.2020.109840