Fractional order SIR epidemic model with Beddington-De Angelis incidence and Holling type II treatment rate for COVID-19.

In this paper, an attempt has been made to study and investigate a non-linear, non-integer SIR epidemic model for COVID-19 by incorporating Beddington-De Angelis incidence rate and Holling type II saturated cure rate. Beddington-De Angelis incidence rate has been chosen to observe the effects of measure of inhibition taken by both: susceptible and infective. This includes measure of inhibition taken by susceptibles as wearing proper mask, personal hygiene and maintaining social distance and the measure of inhibition taken by infectives may be quarantine or any other available treatment facility. Holling type II treatment rate has been considered for the present model for its ability to capture the effects of available limited treatment facilities in case of Covid 19. To include the neglected effect of memory property in integer order system, Caputo form of non-integer derivative has been considered, which exists in most biological systems. It has been observed that the model is well posed i.e., the solution with a positive initial value is reviewed for non-negativity and boundedness. Basic reproduction number is determined by next generation matrix method. Routh Hurwitz criteria has been used to determine the presence and stability of equilibrium points and then stability analyses have been conducted. It has been observed that the disease-free equilibrium is stable for i.e., there will be no infection in the population and the system tends towards the disease-free equilibrium and for , it becomes unstable, and the system will tend towards endemic equilibrium . Further, global stability analysis is carried out for both the equilibria using . Lastly numerical simulations to assess the effects of various parameters on the dynamics of disease has been performed.