QMRA for Drinking Water: 1. Revisiting the Mathematical Structure of Single-Hit Dose-Response Models

Area of Science:

• Environmental microbiology
• Risk assessment
• Mathematical modeling

Background:

• Dose-response models are crucial for quantitative microbial risk assessment (QMRA), linking pathogen exposure to health risks.
• Single-hit models like exponential and beta-Poisson are widely used in drinking water studies.
• Existing models often simplify host susceptibility and pathogen infectivity.

Purpose of the Study:

• To develop a general mathematical single-hit framework for QMRA.
• To explicitly account for variations in host susceptibility and pathogen infectivity.
• To precisely interpret single-hit probability and identify statistical independence assumptions.

Main Methods:

• Developed a general mathematical single-hit framework.
• Incorporated variations in host susceptibility and pathogen infectivity.
• Utilized probability generating and moment generating functions for analysis.

Main Results:

• Variation in host susceptibility reduces single-hit risk compared to constant susceptibility.
• Complete host immunity is represented by a simple scaling of the response.
• Model-consistent expressions for repeated exposures and mean per-exposure dose were derived.

Conclusions:

• The refined framework provides a more precise interpretation of single-hit models.
• Accounting for biological variability leads to more accurate risk assessments.
• New expressions offer improved calculations for repeated exposures and dose determination.