Epidemic threshold of a COVID-19 model with gaussian white noise and semi-Markov switching

In this study, we investigate the COVID-19 propagation dynamics using a stochastic SIQR model with Gaussian white noise and semi-Markovian switching, focusing on the impacts of Gaussian white noise and semi-Markovian switching on the propagation dynamics of COVID-19. It is suggested that the fate of COVID-19 is entirely determined by the basic reproduction number [Formula: see text] , under mild extra conditions. By making sensitivity analysis on [Formula: see text] , we found that the effect of quarantine rate on [Formula: see text] was more significant compared to transmission rate. Our results demonstrate that: (i) The presence of Gaussian white noise, while reducing the basic reproduction number [Formula: see text] of COVID-19, also poses more challenges for the prediction and control of COVID-19 propagation. (ii) The conditional holding time distribution has a significant effect on the kinetics of COVID-19. (iii) The semi-Markov switching and Gaussian white noise can support irregular recurrence of COVID-19 outbreaks.