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

Abstract

A novel coronavirus, designated as COVID-19, emerged 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 coupling 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, infected and hospitalized) are firstly taken into account in the proposed model. And infectivity of individuals during incubation is also considered in this paper. By applying least squares method and predictor-correctors scheme, the numerical solutions of the proposed system in the absence of the inter-city network and with the inter-city network are stimulated by using the real-data from 23 January to 18 − m March, 2020 where m is equal to the number of prediction days. Compared with integer-order system (α = 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 without 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 uniqueness of a bounded solution under the initial condition are considered in the proposed system. Afterwards, the basic reproduction number R 0 is analyzed and it is found to hold a threshold: the disease-free equilibrium point is locally asymptotically stable when R 0 ≤ 1, which provides a theoretical basis for whether COVID-19 will become a pandemic in the future.

The dynamics of COVID-19 with quarantined and isolation

“…In another study, the authors studied the dynamics of COVID-19 in Italy [ 3 ]. A fractional model for intercity network is considered in [ 4 ]. A mathematical model of COVID-19 and its simulations are considered in [ 5 ].…”

A fractional-order SIRD model with time-dependent memory indexes for encompassing the multi-fractional characteristics of the COVID-19

“…The SIRD system (2) represents a Markovian process where the previous states do not affect the current conditions, i.e., a memoryless SIRD system. Nevertheless, the network-like human interactions (including the COVID-19) evolve to a pattern with memory properties were past events impact recent events [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . To cope with that, we apply the fractional-order calculus as a mechanism to represent the memory of the biological system since the fractional-order derivative operators represent more accurately the real phenomena in nature [17] , [18] .…”

“…In both cases, they are ”full-memory indexes” because their contributions are since the initial conditions. In literature, recent works have proposed fractional-order mathematical models for studying the COVID-19 [19] , [20] , [21] , [22] , [23] , [24] , [25] , [26] , [27] . Based on the fractional-order derivative with singular kernel we found that Rezapour et al.…”

“…analyzed the transmission of perturbations across the amino acids of a protein represented as an interaction network applying the Caputo derivative in a SI model [26] ; and Lu et al. presented a fractional SEIHDR model based on the coupling effect of inter-city networks to cope with the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period [27] .…”

A report on COVID-19 epidemic in Pakistan using SEIR fractional model

“…Yadav and Verma 9 examined the spread of COVID-19 in Wuhan, China through a dynamical CF fractional model with different classes and shown the effect of concentration of virus in the surrounding environment on these classes. Lu et al 10 investigated the dynamics of COVID-19 in different high concentrated cities of China using Caputo fractional model with six different compartments. Rajagopal et al 11 investigated the dynamics of COVID-19 in Italy using Caputo fractional model.…”