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Epidemic dynamics in finite size scale-free networks
Romualdo Pastor-Satorras1, Alessandro Vespignani
1Departament de Física i Enginyeria Nuclear, Universitat Politècnica de Catalunya, Campus Nord B4, 08034 Barcelona, Spain.
Summary
Epidemic dynamics in bounded scale-free networks are significantly impacted by connectivity cutoffs. Neglecting these fluctuations overestimates epidemic thresholds, even in smaller networks.
Area of Science:
- Network Science
- Epidemiology
- Statistical Physics
Background:
- Real-world networks often exhibit bounded scale-free properties due to physical limitations or finite size.
- Connectivity cutoffs are common in these networks, influencing their structure and dynamics.
- Understanding epidemic spread in such constrained networks is crucial for public health and network management.
Purpose of the Study:
- To investigate epidemic dynamics in bounded scale-free networks with both soft and hard connectivity cutoffs.
- To analyze the impact of finite size effects and connectivity fluctuations on epidemic thresholds.
- To derive expressions for infection prevalence and their finite size corrections.
Main Methods:
- Mathematical modeling of epidemic spread on bounded scale-free networks.
- Analysis of network properties considering soft and hard connectivity cutoffs.
- Derivation of analytical expressions for infection prevalence and epidemic thresholds.
Main Results:
- Finite size effects introduced by connectivity cutoffs lead to an epidemic threshold that approaches zero with increasing network size.
- Even small cutoffs result in a very small induced epidemic threshold.
- Homogeneous approximations significantly overestimate epidemic thresholds in these heterogeneous networks.
Conclusions:
- The presence of connectivity cutoffs in bounded scale-free networks drastically reduces epidemic thresholds.
- Accurate modeling requires accounting for connectivity fluctuations and finite size effects.
- Homogeneous approximations are inadequate for analyzing epidemic spread in scale-free networks, even with a moderate number of nodes.
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