Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19

Abstract

Developing algorithms for solving high-dimensional uncertain differential equations has been an exceedingly difficult task. This paper presents an α-path-based approach that can handle the proposed high-dimensional uncertain SIR model. We apply the α-path-based approach to calculating the uncertainty distributions and related expected values of the solutions. Furthermore, we employ the method of moments to estimate parameters and design a numerical algorithm to solve them. This model is applied to describing the development trend of COVID-19 using infected and recovered data of Hubei province. The results indicate that lockdown policy achieves almost 100% efficiency after February 13, 2020, which is consistent with the existing literatures. The high-dimensional α-path-based approach opens up new possibilities in solving high-dimensional uncertain differential equations and new applications.