Epidemic dynamics and wealth inequality under two feedback control strategies

A multi-agent wealth exchange model, which considers a varying trading propensity and a control of wealth inequality, is adopted to investigate the wealth distribution under infectious disease. Using the feedback control method, two saturated nonlinear incidence rates are obtained to explore the impact of the government contact control measures on epidemic dynamics and wealth distribution. We find that the contact control measures may reduce the peak of the infected fraction and make more people remain uninfected, but prolong the duration of the epidemic and increase wealth inequality. In a closed (an open) economy, the large-time behavior of wealth distribution presents a Pareto tail, and examples of trading propensity depending on wealth suggest that an increase in the savings of the wealthy may increase wealth inequality. In addition, our simulation results illustrate that the government’s tax and redistribution measures can alleviate the wealth inequality caused by the contact control and improve the wealth of agents at low and middle levels.

Keywords

wealth distribution, infectious disease, dynamic equations, feedback controls, nonlinear incidence rate

2010 Mathematics Subject Classification

35Q20, 35Q84, 35Q93, 91B80

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This research is supported by the National Natural Science Foundation of China (No. 11471263), and by the Sichuan Science and Technology Program (Grant No. 2023NSFSC1343).

Received 2 September 2022

Received revised 19 April 2023

Accepted 6 May 2023

Published 7 December 2023