Mathematical model establishment and simulation analysis of the spread of COVID-19 epidemic

Abstract

In order to explore the intrinsic laws of the spread of COVID-19 across the globe, this paper applies partial differential equation and related theories to model and carry out theoretical analysis and numerical analysis. Firstly, by adding the free diffusion term to the traditional ordinary differential SEIRS epidemic model, the corresponding partial differential epidemic model is established. Secondly, the basic reproduction number R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is calculated by using operator theory and spectral method, and it is testified that R <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> is monotonically decreasing with respect to the diffusion coefficients of the exposed and infected individuals. Furthermore, we examine the asymptotic property of the endemic equilibrium with respect to the diffusion coefficient. Finally, we take the Canadian epidemic data as an example to carry out numerical simulation and parameter sensitivity analysis by applying difference method and BP neural network, the results show that strengthening the isolation of susceptible and exposed individuals, reducing the infection rate of infected individuals will help to better control the large-scale outbreak of the epidemic.