Solutions of a disease model with fractional white noise

被引：30

作者：

Akinlar, M. A. ^{[1
]}

Inc, Mustafa ^{[2
,3
]}

Gomez-Aguilar, J. F. ^{[4
]}

Boutarfa, B. ^{[5
]}

机构：

[1] Yildiz Tech Univ, Dept Math Engn, Istanbul, Turkey

[2] Firat Univ, Dept Math, Fac Sci, TR-23119 Elazig, Turkey

[3] China Med Univ, China Med Univ Hosp, Dept Med Res, Taichung, Taiwan

[4] CENIDET, CONACyT Tecnol Nacl Mexico, Interior Internado Palmira S-N, Cuernavaca 62490, Morelos, Mexico

[5] Guelma Univ, Dept Mat Sci, Guelma 24000, Algeria

来源：

CHAOS SOLITONS & FRACTALS | 2020年 / 137卷

关键词：

DIFFERENTIAL-EQUATIONS; SIR MODEL; CALCULUS;

D O I：

10.1016/j.chaos.2020.109840

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. © 2020 Elsevier Ltd

引用

页数：8

共 52 条

[41] Stochastic integration with respect to multifractional Brownian motion via tangent fractional Brownian motions [J].