Analysis on Infection Wave and Decay of Transmission Risk Based on Spatial SIR Model - Taking COVID Epidemic as an Example

Abstract

Starting with the spatial SIR model, this paper gives the strict boundary conditions, and obtains two theorems in the process of infectious disease transmission through theoretical analysis. After that, the partial differential equations are transformed into ordinary differential equations by the method of traveling wave solution, and the solutions of infectious wave velocity and hypergeometric function are further derived. Beside local diffusion operator model, the paper also developed global transmission risk functions as convolution kernels and discovered their properties. The solution of the spatial infectious disease model is visualized by programming, and the influence of parameter changes on the solution is discussed. Finally, some variants of the model in special cases are given. This paper proves that under generalized assumption the three population densities of the spatial SIR model results at the origin cannot take extreme values at the same time, and when the infected density takes extreme values at the origin, the higher-order derivative of the infected density to the space is zero. The hypergeometric function method verifies the solution at infinity of the equations, and the above solution can be used to approximate when the distance from the infection source radius is large. In this paper, the discussion on the impact of the changes of several infectious disease parameters can inspire the methods of epidemic prevention and control.