Fractional order epidemic model for the dynamics of novel COVID-19

To curtail and control the pandemic coronavirus (Covid-19) epidemic, there is an urgent need to understand the transmissibility of the infection. Mathematical model is an important tool to describe the transmission dynamics of any disease. In this research paper, we present a mathematical model consisting of a system of nonlinear fractional order differential equations, in which bats were considered as the origin of the virus that spread the disease into human population. We proved the existence and uniqueness of the solution of the model by applying Banach contraction mapping principle. The equilibrium solutions (disease free & endemic) of the model were found to be locally asymptotically stable. The key parameter (Basic reproduction number) describing the number of secondary infections was obtained. Furthermore, global stability analysis of the solutions was carried out using Lyapunov candidate function. We performed numerical simulation, which shows the changes that occur at every time instant due to the variation of α . From the graphs, we can see that FODEs have rich dynamics and are better descriptors of biological systems than traditional integer – order models.