Control and Anticontrol of chaos in Fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola Virus diseases.

This work proposes new fractional-order (FO) models of six chaotic diseases whose fractional dynamics have not been studied so far in literature. Secondly, design and analysis of suitable controllers to control chaos where present, and that of anticontrollers to generate chaos where absent, for these newly proposed FO models of diseases, are put forward. The proposed controllers and anticontrollers address the problem of the health hazards arising from the dysfunctionalities due to the impact of chaos in these biological models. Controllers to supress chaos in four diseases, namely, FO Diabetes Mellitus, FO Human Immunodeficiency Virus (HIV), FO Ebola Virus and FO Dengue models are designed by Back-stepping, Adaptive Feedback and Sliding Mode Control strategies, whereas anticontrollers to introduce chaos in diseases, namely, FO Parkinson's illness and FO Migraine models, are carried out by Linear State Feedback, Single State Sinusoidal Feedback and Sliding Mode Anticontrol strategies. The equilibrium points, eigenvalues and Lyapunov Exponents of the FO disease models are evaluated and indicate the significance of chaos in them and necessitate upon the requirement of controllers and anticontrollers accordingly. The simulation results in terms of bifurcation diagrams, time series plots and phase portraits confirm the successful accomplishment of the control objectives.