Dynamics of a stochastic delay differential model for COVID-19 infection with asymptomatic infected and interacting people: Case study in the UAE

Public health science is increasingly focusing on understanding how COVID-19 spreads among humans. For the dynamics of COVID-19, we propose a stochastic epidemic model, with time-delays, Susceptible–Infected–Asymptomatic–Quarantined–Recovered (SIAQR). One global positive solution exists with probability one in the model. As a threshold condition of persistence and existence of an ergodic stationary distribution, we deduce a generalized stochastic threshold R₀^s<R₀. To estimate the percentages of people who must be vaccinated to achieve herd immunity, least-squares approaches were used to estimate R₀ from real observations in the UAE. Our results suggest that when R₀>1, a proportion max(1−1/R₀) of the population needs to be immunized/vaccinated during the pandemic wave. Numerical simulations show that the proposed stochastic delay differential model is consistent with the physical sensitivity and fluctuation of the real observations.