Estimating the initial relative infection rate for a stochastic epidemic model

Area of Science:

• Epidemiology
• Stochastic modeling
• Biostatistics

Background:

• Analyzing infectious disease data relies on assumptions about disease progression.
• Non-random latent and infectious periods simplify epidemic modeling.
• Accurate estimation of initial infection rates is crucial for understanding disease spread.

Purpose of the Study:

• To develop and compare martingale-based methods for estimating the initial relative infection rate in stochastic epidemic models.
• To derive explicit formulas for parameter estimates and their standard errors.
• To assess the performance of these methods using real-world data.

Main Methods:

• Utilized two martingale-based techniques for statistical inference.
• The first method requires complete epidemic data; the second uses aggregated data (total infected, population size).
• Derived explicit expressions for parameter estimates and standard errors.

Main Results:

• Obtained easily computable estimates and standard errors for the initial relative infection rate.
• Demonstrated the effectiveness of the methods through an application to smallpox data.
• Compared the computational ease and accuracy against existing methods.

Conclusions:

• Martingale techniques offer efficient and practical approaches for estimating initial infection rates in epidemic models.
• The methods are applicable to both complete and aggregated epidemic data.
• These findings contribute to improved infectious disease data analysis and modeling.