Extended SEIR model of COVID-19 spread focusing on compartmental flow in England

We propose an extended SEIR epidemic model for assessing the spread of COVID-19 during an outbreak. Our model consists of a system of ordinary differential equations with eight state variables, emphasizing the movement of individuals across three social domains: households, communities, and hospitals. This model breaks through the assumption in previous SEIR models that the population follows a homogeneous spatial distribution, and offers a different approach for studying the spread of infectious diseases. Such mathematical properties of our model are demonstrated as basic reproduction number, the existence and local stability of the disease-free equilibrium and endemic equilibrium point. We calibrate the model parameters using the Markov Chain Monte Carlo method and reproduce the spread of the Delta variant outbreak in England, exhibiting the validity and effectiveness of our extended model. The control measures are suggested by conducting a sensitivity analysis, which provides some management implications for controlling COVID-19 in England.