Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19
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Numerical solution and parameter estimation for uncertain SIR model with application to COVID-19 Xiaowei Chen1
· Jing Li2 · Chen Xiao1 · Peilin Yang1
Accepted: 7 September 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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 αpath-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. Keywords Uncertainty theory · Uncertain differential equation · SIR model · COVID-19
1 Introduction The World Health Organization (WHO) defines a pandemic as the worldwide spread of a new disease. Since December 2019, the COVID-19 causes infection of over 10
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Jing Li [email protected] Xiaowei Chen [email protected] Chen Xiao [email protected] Peilin Yang [email protected]
1
School of Finance, Nankai University, Tianjin 300350, China
2
School of Mathematical Sciences, Nankai University, Tianjin 300071, China
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X. Chen et al.
million people and over 500K deaths by Jun 30, 2020. The widespread epidemics have a profound historical impact on economic and social development, leading directly to less confidence in economic growth and a sharp drop in investment. The 1918 Spanish flu infected about 500 million people worldwide. The 1957 Asian influenza pandemic killed at least 1 million people. According to World Bank officials, the 1968 Hong Kong flu could cause global GDP to fall by 0.7% in the first year. The 2002 SARS caused a productivity loss of more than 40 billion US dollars. The epidemics hit trade and services hard. The World Bank estimates that the SARS epidemic caused 54 billion US dollars to the global economy, while the 2009 Influenza A (H1N1) pandemic caused between 45 and 55 billion US dollars in global losses. Besides the economic impact, the decline in human capital indirectly affected economic activity in the decades following the pandemic. In fact, the poor suffered the most significant impact, which exacerbated social inequality. Besides, the epidemic not only causes economic depression, but also causes patients and their families to be isolated and stigmatized, and suffering high psychological stress. Researchers urgently need to establish mathematical models to predict pandemic trends and formulate better prevention, control, and res
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