  Covid-19 is one of the most dreaded pandemics/epidemics in the world
threatening the human population. The dynamics of this pandemic is quite
complicated and prediction of pandemic states often fails. In this work, we
study and correlate the SIR epidemiological model with the ongoing pandemic and
found that pandemic dynamics and states are quite sensitively dependent on
model parameters. The analysis of the exact parametric solution of the
deterministic SIR model shows that the fixed points ($g^*$) depend on the SIR
parameters, where, if $g^*\langle\frac{\gamma}{\beta x_0}$ then $g^*$ is stable
and the pandemic can be controlled, whereas, if $g^*\rangle\frac{\gamma}{\beta
x_0}$ then $g^*$ is unstable indicating active pandemic state, and $g^*=0$
corresponds to an endemic state. The dynamics show asymptotic stability
bifurcation. The analytical solution of the stochastic SIR model allows to
predict endemic time $t_E\propto\frac{1}{\gamma}$ and mean infected population
becomes constant for small values of $\gamma$. The noise in the system even can
modulate pandemic dynamics. Hence, we estimated the values of these parameters
during lockdown periods using the ABC SSA algorithm and found strong dependence
on control strategy, namely, lockdown and follows power-law behaviors. The
numerical results show strong agreement with the real data and have the
positive effect of social distancing or lockdown in the pandemic control.
