Dynamics and Control Measures of a Stochastic SEIQR Model for the COVID-19 Epidemic

Abstract

To capture the transmission dynamics of COVID-19, we develop a novel stochastic SEIQR infectious disease model with a latent period and isolation. Firstly, we prove the existence and uniqueness of a global solution for the stochastic epidemic model. Additionally, we determine the threshold values  $R_{i}^{s}(i=1,2)$  of the stochastic model. If  $R_{1}^{s}<1$, the disease will inevitably become extinct with probability one and stochastically persistent if  $R_{2}^{s}>1$. To control the spread of the disease, we implement vaccination and treatment measures within the stochastic model and ultimately achieve the optimal strategies. Numerical simulations are conducted to validate the analytical results for the model with and without control. Finally, we apply the stochastic model to analyze the outbreak of the COVID-19 epidemic in Saudi Arabia.