Fractional order modelling of Anthrax-Listeriosis coinfection with nonsingular Mittag Leffler law

Abstract

Anthrax and Listeriosis are both bacteria infections that affect the human system in different ways. This study, analyses a fractional order model of Anthrax-Listeriosis coinfection. The model is a modification of the integer order model formulated by Osman and Makinde in [1]. The positivity, existence and uniqueness of the model solutions are investigated by applying the definition of the Atangana-Baleanu (AB) operator in the sense Louiville-Caputo to the model. The Hyers-Ulam stability analysis is carried out and the model is proven to be Hyers-Ulam stable. The Adams-mouton scheme for the proposed (AB) coinfection model is derived and used to numerically simulate the theoretical results by varying fractional orders to see how changes in the fractional order derivative affects the coinfection dynamics. The results obtained are in agreement with the results obtained in the corresponding integer model by Osman and Makinde, however, the results reveal that the fractional order is the main driver of the coinfection and that the use of the ABC operator and fractional operators in general enhances a better description of biological processes than integer order operators.

Keywords

• Anthrax
• Listeriosis
• Atangana Baleanu-Caputo operator
• Fractional derivative
• Coinfection