The impact of Caputo-Fabrizio operator on the complex dynamics of a multidrug resistance model

This work studied the impact of Caputo–Fabrizio derivatives on the chaotic dynamics in a multidrug resistance dynamical system. The local stability conditions of the drug-free, healthy, and multidrug resistance equilibrium states are proven. The numerical simulations demonstrate the presence of chaos in the considered fractional model and its integer-order counterpart, which means that the coexistence of both susceptible and infected populations is highly unpredictable because of the multidrug resistance. Furthermore, the consistency between the fractional system and its integer-order counterpart is evident for a wide time scale, despite the use of two different numerical algorithms. The new numerical algorithm for integrating the fractional model is presented, along with proofs of its conditional stability and convergence. In addition, the study used advanced software tools, such as bifurcation diagrams based on the local maxima algorithm and Lyapunov spectrum, that confirm the regions of chaos and their distribution in these systems when the growth rate of the susceptible population changes within a certain range.