Uncertain SEIAR model for COVID-19 cases in China
- PDF / 334,530 Bytes
- 17 Pages / 439.37 x 666.142 pts Page_size
- 97 Downloads / 150 Views
Uncertain SEIAR model for COVID-19 cases in China Lifen Jia1 · Wei Chen1 Accepted: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The Susceptible-Exposed-Infectious-Asymptomatic-Removed (SEIAR) epidemic model is one of most frequently used epidemic models. As an application of uncertain differential equations to epidemiology, an uncertain SEIAR model is derived which considers the human uncertainty factors during the spread of an epidemic. The parameters in the uncertain epidemic model are estimated with the numbers of COVID-19 cases in China, and a prediction to the possible numbers of active cases is made based on the estimates. Keywords Uncertainty theory · Uncertain differential equation · Uncertain SEIAR model · COVID-19 · Parameter estimation
1 Introduction Epidemics have always been a threat to human health. To describe and predict the spread of an epidemic, various models have been built such as the SIS model, SIR model, SEIR model and SEIAR model. Since the establishment of stochastic differential equation theory in 1950s, stochastic epidemic models have been investigated for the reasons of indeterminate factors during the spread process of an epidemic. For example, Gray et al. (2011) presented a stochastic SIS model, and gave some conditions for extinction and persistence of the disease. Ji et al. (2012) discussed a stochastic SIR model, and proved the stability conditions of disease-free equilibrium. Artalejo et al. (2015) presented a stochastic SEIR model, and studied the evolution of the epidemic before its extinction. As we know, stochastic differential equations are applicable to dynamic systems with random factors rather than human uncertainty, so it is questionable whether they can properly describe epidemic systems which are heavily affected by human behaviors.
B 1
Wei Chen [email protected] School of Management and Engineering, Capital University of Economics and Business, Beijing, China
123
L. Jia, W. Chen
As a branch of mathematics for modelling human uncertainty, the uncertainty theory was founded by Liu (2007) and perfected by Liu (2009). Within the framework of uncertainty theory, the concept of uncertain differential equation was proposed by Liu (2008) to describe dynamic systems with human uncertainty. Chen and Liu (2010) gave a sufficient condition for an uncertain differential equation to have a unique solution, and Yao et al. (2013) proved some stability theorems about uncertain differential equations. The structure of the solution of an uncertain differential equation was found by Yao and Chen (2013), based on which various numerical methods have been designed to solve uncertain differential equations, such as Yang and Ralescu (2015), Gao (2016), and Zhang et al. (2017). In order to estimate the parameters in uncertain differential equations based on observed data, Yao and Liu (2020) presented the method of moments, which was extended to the generalized method of moments by Liu (2020). In addition, the least squares estimation a
Data Loading...
