Herd immunity under individual variation and reinfection

Area of Science:

• Epidemiology
• Mathematical Biology
• Infectious Disease Modeling

Background:

• The susceptible-exposed-infected-recovered (SEIR) model is a standard framework for studying infectious disease dynamics.
• Previous models often assume homogeneous populations, which may not reflect real-world scenarios.
• Heterogeneity in individual susceptibility or exposure can significantly impact epidemic spread and herd immunity.

Purpose of the Study:

• To investigate the impact of heterogeneity in susceptibility or exposure on herd immunity thresholds within an SEIR model.
• To derive explicit mathematical formulas for calculating herd immunity thresholds and stable configurations in heterogeneous populations.
• To explore extensions of the SEIR model incorporating gamma-distributed susceptibility or exposure.

Main Methods:

• Utilized a susceptible-exposed-infected-recovered (SEIR) compartmental model.
• Incorporated heterogeneity in susceptibility and/or exposure to infection among individuals.
• Derived analytical formulas for herd immunity thresholds and stable population states.
• Applied gamma distribution to model variations in susceptibility or exposure.

Main Results:

• Epidemic growth is suppressed below the herd immunity threshold in heterogeneous populations.
• The herd immunity threshold is lower in heterogeneous populations compared to homogeneous ones.
• Explicit formulas were derived for calculating herd immunity thresholds, particularly for gamma-distributed parameters.
• The study explored potential extensions to the heterogeneous SEIR model.

Conclusions:

• Heterogeneity in susceptibility or exposure is a critical factor in determining herd immunity thresholds.
• The derived formulas provide a quantitative tool for estimating herd immunity in diverse populations.
• Understanding these thresholds is crucial for effective public health interventions and epidemic control strategies.