Sensitivity analysis of epidemic forecasting and spreading on networks with probability generating functions

Area of Science:

• Epidemiology
• Mathematical Biology
• Computational Statistics

Background:

• Epidemic forecasting models utilize stochasticity and heterogeneity to predict disease spread.
• Probability generating functions (PGFs) are efficient mathematical tools for describing these models.
• Traditional sensitivity analyses are computationally expensive for complex epidemic models.

Purpose of the Study:

• To develop and apply statistical condition estimation to assess the sensitivity of PGF-based epidemic forecasts.
• To differentiate forecast stochasticity from input data noise.
• To understand how transmission homogeneity affects forecast sensitivity.

Main Methods:

• Utilized statistical condition estimation to analyze noisy PGFs.
• Modeled epidemic spread using branching processes and contact networks.
• Investigated sensitivity across various basic reproduction numbers ($R_0$) and dispersion parameters ($k$).

Main Results:

• Forecast sensitivity is highest at the epidemic threshold ($R_0 = 1$) for homogeneous transmission ($k > 0.3$).
• In heterogeneous systems ($k ","leq" 0.3$), peak sensitivity occurs for $R_0 > 1$.
• The methods successfully separate forecast stochasticity from input noise.

Conclusions:

• The developed methods enhance the transparency of PGF-based epidemic forecasting.
• Understanding sensitivity is crucial for reliable predictions, especially near the epidemic threshold.
• These findings are applicable to a wide range of epidemic models using PGFs.