Estimating initial epidemic growth rates.

Area of Science:

• Epidemiology
• Mathematical Biology
• Biostatistics

Background:

• Initial epidemic growth rate is crucial for understanding disease spread and estimating the basic reproduction number.
• Maximum likelihood fitting of phenomenological models offers a simpler alternative to complex mechanistic models, especially with limited data.
• Selecting the appropriate phenomenological model for epidemic data is often challenging.

Purpose of the Study:

• To compare the performance of four common phenomenological models (exponential, Richards, logistic, delayed logistic) for estimating initial epidemic growth rates.
• To evaluate model accuracy in point estimates and confidence interval coverage using simulated epidemic data.
• To determine the best-performing models for both incidence and mortality data.

Main Methods:

• Simulated epidemic data with known parameters were generated.
• Four phenomenological models (exponential, Richards, logistic, delayed logistic) were fitted using maximum likelihood estimation.
• Model performance was assessed based on accuracy of growth rate estimates and confidence interval properties (width and coverage).

Main Results:

• For incidence data, the logistic and Richards models provided accurate estimates up to the epidemic peak.
• The Richards model demonstrated superior confidence interval coverage with small observation errors.
• For mortality data, the Richards and delayed logistic models yielded the most accurate growth rate estimates.

Conclusions:

• The Richards and logistic models are recommended for estimating initial epidemic growth rates from incidence data.
• The Richards and delayed logistic models are preferable for analyzing mortality data.
• Accurate initial growth rate estimation depends on the data type (incidence vs. mortality) and the chosen phenomenological model.