A coinfected modeling of anthrax and listeriosis with power law

Abstract

Coinfections are difficult to manage and control due to the different complexities of the diseases. In this study, we analyse the fractional order version of the Anthrax-Listeriosis coinfection model formulated by Osman and Makinde in [1]. We investigate the positivity, existence and uniqueness of the model solutions and use the Liouville-Caputo operator to perform stability analysis of the model. The Adams-type predictor corrector method is also employed to analyse the trajectories of the model. We numerically simulate the theoretical results by varying fractional orders to see how changes in the fractional order derivative affects the coinfection dynamics. Our results indicate that the model notably depends on the fractional order derivative and model parameters. It also suggests that the fractional order is the main driver of the coinfection. The results we obtained are hand in glove with the results obtained in the corresponding integer model by Osman and Makinde, however, our results reveal that the use of the Liouville Caputo operator and fractional operators in general enhance a better description of biological processes than integer order operators.