Authors: Tom Cuchta; Sabrina Streipert
Addresses: Department of Computer Science and Math, Fairmont State University, 1201 Locust Avenue, Fairmont, WV, 26554, USA ' Department of Mathematics and Statistics, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4K1, Canada
Abstract: In this work, we introduce two epidemic fractional difference equation models and derive their explicit solutions. The presented model is of the Susceptible-Infected-Susceptible class, which assumes that the disease is spread from susceptible to infected individuals who join the group of susceptible after recovery. The model is constructed using the fractional difference operators defined in Goodrich and Peterson (2015), which sets it apart from the few existing discrete fractional epidemic model formulations. The unique solution of the presented fractional difference epidemic models is derived and relations to existing discrete SIS models are discussed.
Keywords: fractional difference equations; Riemann-Liouville difference; difference equations; Nabla-difference equations; epidemic model; SIS; explicit solution; unique solution.
International Journal of Dynamical Systems and Differential Equations, 2021 Vol.11 No.3/4, pp.275 - 286
Received: 24 Apr 2020
Accepted: 14 Jul 2020
Published online: 01 Sep 2021 *