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Robustness and fragility of the susceptible-infected-susceptible epidemic models on complex networks
Wesley Cota1, Angélica S Mata2, Silvio C Ferreira1,3
1Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil.
Abstract:
We analyze two alterations of the standard susceptible-infected-susceptible (SIS) dynamics that preserve the central properties of spontaneous healing and infection capacity of a vertex increasing unlimitedly with its degree. All models have the same epidemic thresholds in mean-field theories but depending on the network properties, simulations yield a dual scenario, in which the epidemic thresholds of the modified SIS models can be either dramatically altered or remain unchanged in comparison with the standard dynamics. For uncorrelated synthetic networks having a power-law degree distribution with exponent γ<5/2, the SIS dynamics are robust exhibiting essentially the same outcomes for all investigated models. A threshold in better agreement with the heterogeneous rather than quenched mean-field theory is observed in the modified dynamics for exponent γ>5/2. Differences are more remarkable for γ>3, where a finite threshold is found in the modified models in contrast with the vanishing threshold of the original one. This duality is elucidated in terms of epidemic lifespan on star graphs. We verify that the activation of the modified SIS models is triggered in the innermost component of the network given by a k-core decomposition for γ<3 while it happens only for γ<5/2 in the standard model. For γ>3, the activation in the modified dynamics is collective involving essentially the whole network while it is triggered by hubs in the standard SIS. The duality also appears in the finite-size scaling of the critical quantities where mean-field behaviors are observed for the modified but not for the original dynamics. Our results feed the discussions about the most proper conceptions of epidemic models to describe real systems and the choices of the most suitable theoretical approaches to deal with these models.
Insights
This study reveals that modified susceptible-infected-susceptible (SIS) epidemic models exhibit dual behaviors on networks. Depending on network properties, epidemic thresholds can change significantly or remain the same compared to standard SIS dynamics.
Area of Science:
- Epidemiology
- Network Science
- Mathematical Biology
Background:
- The standard susceptible-infected-susceptible (SIS) model is widely used to study epidemic dynamics.
- Understanding how network structure influences epidemic spread is crucial for public health.
- Previous models often assume simplified network properties, potentially limiting their real-world applicability.
Purpose of the Study:
- To analyze two modified SIS epidemic models that retain key properties of spontaneous healing and degree-dependent infection capacity.
- To investigate how network characteristics, specifically degree distribution, affect epidemic thresholds in these modified models compared to the standard SIS model.
- To elucidate the observed dual scenario in epidemic threshold behavior through epidemic lifespan analysis on star graphs.
Main Methods:
- Analysis of two modified susceptible-infected-susceptible (SIS) dynamics on uncorrelated synthetic networks with power-law degree distributions.
- Comparison of epidemic thresholds between modified SIS models and the standard SIS model across different exponent values (γ).
- Investigation of epidemic activation and lifespan on star graphs and k-core decomposition to understand model duality.
Main Results:
- Simulations show a dual scenario where modified SIS models' epidemic thresholds are either dramatically altered or unchanged depending on network properties.
- For power-law networks with γ<5/2, SIS dynamics are robust, showing similar outcomes across models.
- For γ>5/2, modified models show thresholds aligning better with heterogeneous mean-field theory, with significant differences for γ>3, including a finite threshold versus a vanishing one in the standard model.
Conclusions:
- Modified SIS models exhibit a duality in epidemic threshold behavior contingent on network structure, unlike the standard SIS model.
- The activation mechanism of epidemics differs significantly between standard and modified SIS models, especially for higher γ values.
- Results highlight the importance of considering network heterogeneity and choosing appropriate theoretical approaches for realistic epidemic modeling.
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