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A fractional-order SEIHDR model for COVID-19 with inter-city networked coupling effects
Zhenzhen Lu1, Yongguang Yu1, YangQuan Chen2
1Department of Mathematics, Beijing Jiaotong University, Beijing, 100044 People's Republic of China.
Insights
This study introduces a fractional SEIHDR model to analyze COVID-19 spread, incorporating network effects and mortality rates. The model accurately fits data for several regions and offers insights into disease control strategies.
Area of Science:
- Epidemiology and Mathematical Modeling
- Infectious Disease Dynamics
Background:
- The emergence of COVID-19 in late 2019 necessitated advanced modeling techniques to understand its spread.
- Existing models often simplify disease transmission dynamics, failing to capture complex factors like inter-city connectivity and incubation period infectivity.
Purpose of the Study:
- To propose and validate a novel fractional SEIHDR (Susceptible-Exposed-Infectious-Hospitalized-Deceased-Recovered) model for COVID-19.
- To incorporate inter-city network coupling, varying mortality rates, and incubation period infectivity into the epidemiological model.
- To assess the model's predictive accuracy and applicability across different geographical regions and public health interventions.
Main Methods:
- Development of a fractional-order SEIHDR compartmental model.
- Integration of an inter-city network structure to represent population movement.
- Parameter estimation and model fitting using real-world COVID-19 data (Jan-Mar 2020) via least squares and prediction-correction methods.
Main Results:
- The fractional non-network model demonstrated superior data fitting compared to integer-order models for specific Chinese cities.
- The inter-city network model showed limited benefit in China due to strict containment but proved effective for countries without closure measures (e.g., USA, Italy, Japan).
- The model successfully predicted diagnosis peaks and provided theoretical underpinnings for disease control through analysis of the disease-free equilibrium point.
Conclusions:
- Fractional-order modeling offers enhanced accuracy in capturing COVID-19 transmission dynamics, especially when accounting for network effects.
- The model's performance varies based on implemented public health interventions, highlighting the importance of context-specific analysis.
- The study provides a robust mathematical framework for understanding and potentially controlling infectious disease outbreaks.
Abstract:
In the end of 2019, a new type of coronavirus first appeared in Wuhan. Through the real-data of COVID-19 from January 23 to March 18, 2020, this paper proposes a fractional SEIHDR model based on the coupling effect of inter-city networks. At the same time, the proposed model considers the mortality rates (exposure, infection and hospitalization) and the infectivity of individuals during the incubation period. By applying the least squares method and prediction-correction method, the proposed system is fitted and predicted based on the real-data from January 23 to March where m represents predict days. Compared with the integer system, the non-network fractional model has been verified and can better fit the data of Beijing, Shanghai, Wuhan and Huanggang. Compared with the no-network case, results show that the proposed system with inter-city network may not be able to better describe the spread of disease in China due to the lock and isolation measures, but this may have a significant impact on countries that has no closure measures. Meanwhile, the proposed model is more suitable for the data of Japan, the USA from January 22 and February 1 to April 16 and Italy from February 24 to March 31. Then, the proposed fractional model can also predict the peak of diagnosis. Furthermore, the existence, uniqueness and boundedness of a nonnegative solution are considered in the proposed system. Afterward, the disease-free equilibrium point is locally asymptotically stable when the basic reproduction number , which provide a theoretical basis for the future control of COVID-19.
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