On a minimum eradication time for the SIR model with time-dependent coefficients
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- by Jiwoong Jang and Yeoneung Kim;
- Proc. Amer. Math. Soc.
- DOI: https://doi.org/10.1090/proc/17156
- Published electronically: April 14, 2025
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Previous version: Original version posted April 14, 2025
Corrected version: This version updates the author's grant support information.
Abstract:
We study the minimum eradication time problem for controlled Susceptible-Infected-Recovered (SIR) epidemic models that incorporate vaccination control and time-varying infected and recovery rates. Unlike the SIR model with constant rates, the time-varying model is more delicate as the number of infectious individuals can oscillate, which causes ambiguity for the definition of the eradication time. We accordingly introduce two definitions that describe the minimum eradication time, and we prove that for a suitable choice of the threshold, the two definitions coincide. We also study the well-posedness of time-dependent Hamilton–Jacobi equation that the minimum eradication time satisfies in the viscosity sense and verify that the value function is locally semiconcave under certain conditions.References
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Bibliographic Information
- Jiwoong Jang
- Affiliation: Department of Mathematics, University of Maryland-College Park, 4176 Campus Drive - William E. Kirwan Hall, College Park, Maryland 20742
- MR Author ID: 1537481
- Email: jjang124@umd.edu
- Yeoneung Kim
- Affiliation: Department of Applied Artificial Intelligence, Seoul National University of Science and Technology, 232 Gongneung-ro, Nowon-gu, 01811 Seoul, Republic of Korea
- Email: kimyeoneung@gmail.com
- Received by editor(s): December 27, 2023
- Received by editor(s) in revised form: September 28, 2024, and November 12, 2024
- Published electronically: April 14, 2025
- Additional Notes: The second author was supported by the National Research Foundation of Korea (NRF) grant funded by MSIT, Republic of Korea (RS-2023-00219980, RS-2023-00211503).
- Communicated by: Ryan Hynd
- © Copyright 2025 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
- MSC (2020): Primary 35D40, 34H05; Secondary 35B99, 35F21
- DOI: https://doi.org/10.1090/proc/17156