Abstract:
In our highly connected modern world, the dispersion of population is very important
at the time when disease spread to evaluate its nature i.e., whether the disease will
die-out or grow. Therefore, in this paper, SIR (Susceptible–Infected–Recovered) model is
framed to describe the dispersal of population for different patches (communities) which
are interconnected using mean field diffusive coupling. The effect of coupling on the
dynamics of the epidemiology classes among different patches has been investigated. The
dynamics of the epidemiology classes is explored under the environment of symmetric
coupling and asymmetric coupling. It is shown that the synchronization and stability
of Disease Free Equilibrium (or Endemic Equilibrium) can be attained simultaneously
through the mechanism of suppression of oscillations namely amplitude death (AD)
and oscillation death (OD). Irrespective of coupling environment i.e., symmetric and
asymmetric, we have observed the tri-stable state and its transition from different states
through Hopf bifurcation and transcritical bifurcation. The basic reproduction number is
also established for the stability of Disease Free Equilibrium and Endemic Equilibrium.
Through bifurcation analysis, it has been found that the disease can become stable or it
can die out through dispersal of population among patches.
