This work is devoted to establish a modified population model of susceptible and infected (SI) compartments to predict the spread of the infectious disease COVID-19 in Pakistan . We have formulated the model and derived its boundedness and feasibility . By using next generation matrices method we have derived some results for the global and local stability of different kinds of equilibrium points . Also, by using fixed point approach some results of existence of at least one solution are studied . Furthermore, the numerical simulations for various values of isolation parameters corresponding to different fractional order are investigated by using modified Euler's method.