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Robust Inverse Reconstruction of Time-Varying Transmission Rates Across Model Structures and Incidence Forms.

Xiunan Wang1, Hao Wang2

  • 1Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, 37403, USA. xiunan-wang@utc.edu.

Bulletin of Mathematical Biology
|January 29, 2026
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Summary
This summary is machine-generated.

Estimating time-varying transmission rates for diseases like influenza and measles is robust. Common model choices do not significantly alter key dynamics, supporting routine use for forecasting and intervention assessment.

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Area of Science:

  • Epidemiology
  • Mathematical Modeling
  • Infectious Disease Dynamics

Background:

  • Accurate estimation of time-varying transmission rates is crucial for public health.
  • Previous studies suggested these estimates are sensitive to model specification.

Purpose of the Study:

  • To test the sensitivity of transmission rate estimates to common model specifications.
  • To evaluate the robustness of continuous inverse methods for reconstructing transmission dynamics.

Main Methods:

  • Applied a continuous inverse method to weekly influenza and measles incidence data.
  • Compared reconstructions across eight compartmental model structures (SIS, SIR, SEIS, SEIR, and vaccinated variants).
  • Assessed reconstructions across five incidence forms, including mass action and saturated incidence.

Main Results:

  • Transmission rate reconstructions for influenza showed high consistency in peak timing and ordering across models.
  • Amplitude shifts in transmission rates aligned with mechanistic expectations (e.g., attenuation with vaccination).
  • For measles, saturated incidence models preserved the rise-and-fall ordering observed in mass action models.

Conclusions:

  • Inverse transmission rate reconstructions are robust to typical choices in model structure and incidence.
  • These findings support the routine use of inverse methods for interpreting disease transmission, forecasting, and evaluating interventions.