A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects

Lu, Z.; Yu, Y.; Chen, Y.; Ren, G.; Xu, C.; Lu, S.; Yin, Z.

A novel coronavirus, designated as COVID-19, e-merged in Wuhan, China, at the end of 2019. In this paper, a mathematical model is proposed to analyze the dynamic behavior of COVID-19. Based on inter-city networked cou-pling effects, a fractional-order SEIHDR system with the real-data from 23 January to 18 March, 2020 of COVID-19 is discussed. Meanwhile, hospitalized individuals and the mortality rates of three types of individuals (exposed, in-fected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during in-cubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numer-ical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stim-ulated by using the real-data from 23 January to 18 - m March, 2020 where m is equal to the number of predic-tion days. Compared with integer-order system ( = 0), the fractional-order model without network is validated to have a better fitting of the data on Beijing, Shanghai, Wuhan, Huanggang and other cities. In contrast to the case with-out network, the results indicate that the inter-city network system may be not a significant case to virus spreading for China because of the lock down and quarantine measures, however, it may have an impact on cities that have not adopted city closure. Meanwhile, the proposed model better fits the data from 24 February to 31, March in Italy, and the peak number of confirmed people is also predicted by this fraction-order model. Furthermore, the existence and unique-ness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic re-production number R0 is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymp-totically stable when R0 [≤] 1, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.