ABSTRACT
Mathematical modelling in epidemiology is used to analyse the dynamical behaviour and spread of diseases caused by different micro-organisms. Also, it provides the understanding of the underlying mechanisms that influence the spread of disease and help to predict the future situation and even control the pandemic. Epidemic diseases like influenza, plague, cholera, MERS, measles, and Ebola have been affecting individuals as well as human society in many ways. This chapter aims at formulating a fractional-order epidemic model taking into account the impact of quarantine and reinfection to examine the dynamics of the outbreak of COVID-19. The non-local behaviour and hysteresis effect of the fractional-order models is quite significant in understanding the epidemics of disease. The model is initially constructed with integer order differential equations which are then converted to its fractional-order form. The discrete version of the corresponding system is then obtained by employing discretization process. The value estimated for the basic reproduction number is evaluated analytically. Stability analysis and optimal control analysis are performed for the considered SEIQR model. 2The dynamic changes that occur in the system due to some parameters are identified and their impact are presented graphically for suitable values. The chaotic behaviour exhibited by the system is studied with bifurcation diagrams and the impact of varying step size on the dynamics of the different population groups is demonstrated with time-varying plots.
