Infective Susceptible Phase Plane Analysis in the Extended SIR Model-I
Main Article Content
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.
Â
Keywords: Immigration, SIR model, I-S phase plane, Virus Growth, Birth and death Rates, 2nd Order Differential equations.
Downloads
Article Details
COPYRIGHT
Submission of a manuscript implies: that the work described has not been published before, that it is not under consideration for publication elsewhere; that if and when the manuscript is accepted for publication, the authors agree to automatic transfer of the copyright to the publisher.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work
- The journal allows the author(s) to retain publishing rights without restrictions.
- The journal allows the author(s) to hold the copyright without restrictions.