Fractional-Order Modeling of COVID-19 Transmission Dynamics: A Study on Vaccine Immunization Failure

Yan Qiao (), Yuhao Ding, Denghao Pang, Bei Wang and Tao Lu
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Yan Qiao: School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China
Yuhao Ding: School of Internet, Anhui University, Hefei 230601, China
Denghao Pang: School of Internet, Anhui University, Hefei 230601, China
Bei Wang: School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China
Tao Lu: School of Mathematical Sciences, Jiangsu Second Normal University, Nanjing 211200, China

Mathematics, 2024, vol. 12, issue 21, 1-18

Abstract: COVID-19 is an enveloped virus with a single-stranded R N A genome. The surface of the virus contains spike proteins, which enable the virus to attach to host cells and enter the interior of the cells. After entering the cell, the virus exploits the host cell’s mechanisms for replication and dissemination. Since the end of 2019, COVID-19 has spread rapidly around the world, leading to a large-scale epidemic. In response to the COVID-19 pandemic, the global scientific community quickly launched vaccine research and development. Vaccination is regarded as a crucial strategy for controlling viral transmission and mitigating severe cases. In this paper, we propose a novel mathematical model for COVID-19 infection incorporating vaccine-induced immunization failure. As a cornerstone of infectious disease prevention measures, vaccination stands as the most effective and efficient strategy for curtailing disease transmission. Nevertheless, even with vaccination, the occurrence of vaccine immunization failure is not uncommon. This necessitates a comprehensive understanding and consideration of vaccine effectiveness in epidemiological models and public health strategies. In this paper, the basic regeneration number is calculated by the next generation matrix method, and the local and global asymptotic stability of disease-free equilibrium point and endemic equilibrium point are proven by methods such as the Routh–Hurwitz criterion and Lyapunov functions. Additionally, we conduct fractional-order numerical simulations to verify that order 0.86 provides the best fit with COVID-19 data. This study sheds light on the roles of immunization failure and fractional-order control.

Keywords: COVID-19; fractional Caputo derivative; vaccine immunization failure; basic regeneration number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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