  The primary goal of this research is to investigate the impact of delay on
the dynamics of the Susceptible-Exposed-Infected-Recovered-Death and
Susceptible (SEIRDS) model, to which we add a stochastic term to account for
uncertainty in COVID-19 parameter estimations. We run two models, one
deterministic and one stochastic, and show that their solutions exist and are
unique. We also numerically investigate the impact of immunity loss on the
emerging time of a new wave, as well as the necessary condition for the
extinction and persistence of the disease.
