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Volume 14
Issue 7
10.3390/axioms14070487
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Article

The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability

by
Yinchong Wang
1,†,
Wenlian Lu
1,† and
Shouhuai Xu
2,*,†
1
School of Mathematical Sciences, Fudan University, 220 Handan Road, Shanghai 200433, China
2
Department of Computer Science, University of Colorado Colorado Springs, 1420 Austin Bluffs Pkwy, Colorado Springs, CO 80918, USA
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work .
Axioms 2025, 14(7), 487; https://doi.org/10.3390/axioms14070487 (registering DOI)
Submission received: 26 April 2025 / Revised: 17 June 2025 / Accepted: 19 June 2025 / Published: 21 June 2025
Versions Notes

Abstract

In this paper, we propose a new and fairly general network-based contagion dynamics model framework. In the model framework, each node in the network can be in one of multiple secure (or good) and infected (or bad) states. We characterize the dynamics of our model framework, by presenting the following: (i) a sufficient condition under which the dynamics are globally asymptotically stable; (ii) a sufficient condition under which the dynamics are locally asymptotically stable; and (iii) a sufficient condition for the persistence of bad states. Finally, we implemented three operations on the transition diagram. These three operations can help eliminate the bad states and help the model achieve the stability conditions.
Keywords: epidemics; contagion dynamics; complex networks; network science epidemics; contagion dynamics; complex networks; network science

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MDPI and ACS Style

Wang, Y.; Lu, W.; Xu, S. The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability. Axioms 2025, 14, 487. https://doi.org/10.3390/axioms14070487

AMA Style

Wang Y, Lu W, Xu S. The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability. Axioms. 2025; 14(7):487. https://doi.org/10.3390/axioms14070487

Chicago/Turabian Style

Wang, Yinchong, Wenlian Lu, and Shouhuai Xu. 2025. "The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability" Axioms 14, no. 7: 487. https://doi.org/10.3390/axioms14070487

APA Style

Wang, Y., Lu, W., & Xu, S. (2025). The Generalized Multistate Complex Network Contagion Dynamics Model and Its Stability. Axioms, 14(7), 487. https://doi.org/10.3390/axioms14070487

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