Analysis of rubella disease model with non-local and non-singular fractional derivatives

Abstract

In this paper we investigate a possible applicability of the newly establishedfractional differentiation in the field of epidemiology. To do this we extendthe model describing the Rubella spread by changing the derivative with thetime fractional derivative for the inclusion of memory. Detailed analysis ofexistence and uniqueness of exact solution is presented using the Banach fixedpoint theorem. Finally some numerical simulations are showed to underpin theeffectiveness of the used derivative.