Framework of Infective Susceptible Phase Plane Analysis of SIR Model

In the present article an attempt is made to understand the Infected-Susceptible phase plane trajectories, describing the growth of virus in the model of Susceptible, Infected, and Removed (SIR) extended to immigration studies. The growth of virus is described by second order differential equation, in terms of small deviations from the steady state solution of infection. Further the situation for discriminator = 0, obtained in solving the second order differential equation, is described. In this analysis the free parameter, defined in terms of immigrant rate, birth and death rates of virus, is shown to play an important role in the shape of the trajectories in I_S Phase plane. For same values of immigration rate, birth and death rates of virus, all the trajectories approach asymptotically the stable equilibrium point (ratio of death to birth rate of virus, ratio of constant immigration rate to death rate of virus), which is termed as a nodal sink. The effect of different parameters such as size of system of computers, death and birth rates of virus and threshold value of the epidemic on the growth of virus is presented.