5.4 Network models in epidemiology

Networks in epidemiology model how diseases spread through populations. They use nodes to represent individuals and edges to show transmission routes, capturing the complexity of real-world interactions that influence outbreaks.

These models offer advantages over traditional compartmental approaches. They allow for more realistic simulations of disease spread, considering factors like superspreaders and community structures. This enables better-targeted intervention strategies and more accurate predictions of epidemic dynamics.

Network Fundamentals in Epidemiology

Networks in disease transmission

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• Networks in epidemiology represent population structure and interactions enabling modeling of complex disease transmission patterns
• Nodes represent individuals or groups with attributes (age, health status, vaccination status)
• Edges connect nodes showing potential disease transmission routes directed or undirected with weights indicating transmission probability
• Types include contact networks, social networks, and transportation networks (airports, bus stations)
• Network properties affecting disease spread encompass degree, centrality measures, path length, and clustering coefficient

Epidemic models on networks

• Adjacency matrix mathematically represents network structure as square matrix dimensions equal to node count elements indicate connections (1) or absence (0)
• SIR model on networks uses differential equations for each node: $dS_i/dt = -β S_i \sum_{j=1}^N A_{ij} I_j$ $dI_i/dt = β S_i \sum_{j=1}^N A_{ij} I_j - γ I_i$ $dR_i/dt = γ I_i$ $A_{ij}$ is adjacency matrix element
• Discrete-time models employ probability-based transitions between compartments using transition matrices
• Stochastic network models incorporate randomness in disease transmission using Gillespie algorithm for simulations

Network structure impact on spread

• Degree distribution influences epidemic threshold and determines superspreaders (healthcare workers, social butterflies)
• Clustering coefficient affects local disease spread and impacts global epidemic dynamics
• Small-world networks combine high clustering and short path lengths leading to rapid initial spread followed by slower long-term dynamics
• Scale-free networks exhibit power-law degree distribution absence of epidemic threshold in infinite networks
• Community structure impacts disease spread between subgroups crucial for designing targeted interventions (school closures, workplace policies)
• Network rewiring shows dynamic changes in network structure over time influencing disease persistence and endemic states

Network vs compartmental models

• Assumptions differ homogeneous mixing in compartmental models vs heterogeneous contact patterns in network models
• Epidemic threshold depends on average degree in compartmental models influenced by degree distribution in network models
• Disease spread generally faster in network models due to heterogeneity depends on network structure and properties
• Final epidemic size often larger in compartmental models more realistic predictions in network models
• Herd immunity uniform threshold in compartmental models varies based on node importance in network models
• Intervention strategies uniformly applied in compartmental models targeted approaches possible in network models (vaccinating hub nodes)
• Network models limitations include computational complexity for large populations and data requirements for accurate network construction