Complex Dynamics of Fractional Order SIR Model with Carrying Capacity in Discrete Time

In population dynamics, Mathematical modeling plays an important role to understand the infectious disease spreading. It proposes effective theoretical support to control the infectious diseases. Understanding the periodic behaviour of epidemic dynamics is of paramount importance in applications. This paper, discuss the qualitative behaviour of fractional order SIR model in discrete form. Disease Free and Endemic Equilibrium points are obtained along with Basic Reproduction Number(epidemic threshold). Analysis of Local stability of the corresponding system is carried out with help of Jury conditions and eigenvalues of the Jacobian matrix corresponding to each equilibrium point. Time plots, phase portraits, Period doubling bifurcation, Neimark-Sacker bifurcation, reverse bifurcation and Maximal Lyapunov exponents graphs are presented to under-stand the transmission of the system and impact of parameters on the dynamics of the system.