Control and anticontrol of chaos in fractional-order models of Diabetes, HIV, Dengue, Migraine, Parkinson's and Ebola virus diseases

Abstract

This work investigates new fractional-order (FO) models of six chaotic diseases whose fractional dynamics have not been studied so far in literature. Here, we design and analyse suitable controllers to control chaos in these bio- mathematical models that show chaos and require stability; and anticontrollers to generate chaos where it is absent and turbulence may be sought. 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. Chaotic behaviour of vital parameters is characterised by extreme sensitivity, and their slight variations such as fall in density of β – cells, abnormal secretion of insulin in blood, small drop in the number of CD4+T cells, etc. may lead to unpredictable complexities in the models. Also, the evolution of the chaotic attractor in the disease model is revealed only when the bifurcation against the FO parameter is performed, indicating that it is a significant parameter to analyse the progression of a disease. Controllers to supress chaos in FO models of Diabetes Mellitus, Human Immunodeficiency Virus (HIV), Ebola Virus and Dengue models, are designed using Back-stepping, Adaptive Feedback and Sliding Mode Control strategies. Anticontrollers to introduce chaos in FO models of Parkinson's illness and Migraine, are designed using Linear State Feedback, Single State Sinusoidal Feedback and Sliding Mode Anticontrol strategies. The simulation results in terms of bifurcation diagrams, time series plots and phase portraits confirm the successful accomplishment of the control objectives.