Abstract
In this paper, we study the rubella disease model with the Caputo–Fabrizio fractional derivative. The mathematical solution of the liver model is presented by a three-step Adams–Bashforth scheme. The existence and uniqueness of the solution are discussed by employing fixed point theory. Finally some numerical simulations are showed to underpin the effectiveness of the used derivative.
Highlights
Rubella was first described in the mid-eighteenth century
The primary symptom of rubella virus infection is the appearance of a rash on the face which spreads to the trunk and limbs and usually fades after three days [2]
4.1 Numerical method and simulations using the Adams–Bashforth scheme, we present a numerical solution for the rubella model (3)
Summary
Rubella was first described in the mid-eighteenth century. Friedrich Hoffmann made the first clinical description of rubella in 1740, which was confirmed by de Bergen in 1752 and Orlow in 1758 [1]. The primary symptom of rubella virus infection is the appearance of a rash (exanthem) on the face which spreads to the trunk and limbs and usually fades after three days [2]. It usually spreads through the air via coughs of people who are infected. The Caputo fractional derivative of order α for a continuous function f is defined by CDαf (t) = 1 Γ (n – α). Our second notion is a fractional derivative without singular kernel introduced by Caputo and Fabrizio [11, 34]. CFDα+n of order n + α are defined by CFDα+nu(t) := CFDα(Dnu(t)) [26]
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