Time-Delay Dynamic Model and Cost-Effectiveness Analysis of Major Emergent Infectious Diseases with Transportation-Related Infection and Entry-Exit Screening

Yi Xie, Ziheng Zhang, Yan Wu, Shuang Li, Liuyong Pang and Yong Li ()
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Yi Xie: School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
Ziheng Zhang: School of Environment, Education & Development (SEED), The University of Manchester, Manchester M139PL, UK
Yan Wu: College of Applied Sciences, Beijing University of Technology, Beijing 100124, China
Shuang Li: College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China
Liuyong Pang: School of Mathematics and Statistics, Huanghuai University, Zhumadian 463000, China
Yong Li: School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

Mathematics, 2024, vol. 12, issue 13, 1-25

Abstract: We analyze a time-delayed SIQR model that considers transportation-related infection and entry–exit screening. This model aims to determine the measures for preventing and controlling major emergent infectious diseases and the associated costs. We calculate the basic reproduction number ( R 0 ) and prove that the disease-free equilibrium is locally and globally asymptotically stable. We collect COVID-19 infection data from two regions in the United States in 2020 for data fitting, obtain a set of optimal parameter values, and find that transportation-related infection rates increase the basic reproduction number, enhancing the impact on disease spread. Entry–exit screening effectively suppresses the spread of disease by reducing the basic reproduction number. Furthermore, we investigate the influence of the incubation period on disease and find that a shorter incubation period results in a shorter duration but a larger scale of infection and that the peaks are reduced. We conduct a sensitivity analysis of the R 0 and propose three measures to prevent the spread of new infectious diseases based on the most sensitive parameters: wearing masks, implementing urban closures, and administering medication to sick but not yet hospitalized patients promptly. In the case of COVID-19, optimal control effectively controls the development and deterioration of the disease. Finally, several control measures are compared through cost-effectiveness analysis, and the results show that wearing masks is the most cost-effective measure.

Keywords: transportation-related infection; entry-exit screening; basic reproduction number; optimal control; cost-effectiveness (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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