The asymptotic spreading speeds of COVID-19 with the effect of delay and quarantine

Abstract

Coronavirus spread in Wuhan, China, in December 2019. A few weeks later, the virus was present in over 100 countries around the globe. Governments have adopted extreme measures to contain the spreading virus. Quarantine is considered the most effective way to control the spreading speed of COVID-19. In this study, a mathematical model is developed to explore the influence of quarantine and the latent period on the spatial spread of COVID-19. We use the mathematical model with quarantine, and delay to predict the spreading speed of the virus. In particular, we transform the model to a single integral equation and then apply the Laplace transform to find implicit equations for the spreading speeds. The basic reproduction number of COVID-19 is also found and calculated. Numerical simulations are performed to confirm our theoretical results. To validate the proposed model, we compare our outcomes with the actual reported data published by the National Health Commission of China and the Health Commission of local governments. The model demonstrates good qualitative agreement with the actual data reported. The results show that delay and quarantine highly influence the spreading speeds of COVID-19. Also, we can only contain the disease if we quarantine $ 75 \% $ of the infected people.

Keywords

• covid-19
• epidemic model
• spreading speed
• quarantine
• delay model
• numerical simulation