The global existence of the solution to the stage-structured SIR system for rumor spreading and its regularity

Sun-Ho Choi; Hyowon Seo; Minha Yoo

doi:10.3934/eect.2024036

Article Contents

2024, Volume 13, Issue 6: 1460-1485. Doi: 10.3934/eect.2024036

This issue Previous Article Sufficient maximum principle for partially observed mean-field stochastic optimal control problems with delays Next Article Optimal distributed control of the viscous Cahn-Hilliard-Oono system with chemotaxis

The global existence of the solution to the stage-structured SIR system for rumor spreading and its regularity

1.
Department of Applied Mathematics and the Institute of Natural Sciences, Kyung Hee University, Yongin 17104, Republic of Korea
2.
Department of Mathematics, Kunsan National University, Gunsan 54150, Republic of Korea
3.
National Institute for Mathematical Sciences, Daejeon 34047, Republic of Korea

^*Corresponding author: Hyowon Seo
^*Corresponding author: Hyowon Seo

Received: March 2024

Revised: June 2024

Early access: July 2024

Published online: July 2024

H. Seo was supported by research funds of Kunsan National University. M. Yoo was supported by the National Institute for Mathematical Sciences (NIMS) granted by the Korea government (No. NIMS-B24910000).

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Abstract

We consider the global existence and regularity of the solution to the stage-structured SIR system for rumor spreading. To obtain the local existence result of a weak solution to the system, we reduce the system to a single equation using the SIR structure and employ a fixed point argument with a Banach space and Volterra's formula. By defining an appropriate weak solution of the system, we show that the total mass is conserved. Using the local solution to the single equation and the mass conservation property of the system, we verify the global existence of a weak solution to the stage-structured SIR system. If the initial data are regular and satisfy some compatible conditions, then we prove that the solution is piecewise continuously differentiable.

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Mathematics Subject Classification: Primary: 35A01, 35B65; Secondary: 92D15, 92D25.

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