Infective Susceptible Phase Plane Analysis in the Extended SIR Model-I

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N Suresh Rao

Abstract

In the present investigation an attempt is made to understand the I-S phase plane. Trajectories, using the solutions of the second order differential equation, describing the virus growth in the extended model of SIR covering immigration studies, are presented. The value of the ratio of product of immigrant rate and birth rate of virus to square of death rate of virus, greater than or equal to value four, plays a dominant role in deciding the nature of I-S trajectories. For same values of immigration rate, birth and death rates of virus the trajectories reach asymptotically the stable equilibrium point (ratio of death and birth rate of virus, ratio of immigration and death rate of virus) which is termed as a nodal sink. Effect of low and high values of death rate, birth rate and threshold value along with different population sizes is also illustrated therein.

 

Keywords: Immigration, SIR model, I-S phase plane, Virus Growth, Birth and death Rates, 2nd Order Differential equations.

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