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Quantifying indirect and direct vaccination effects arising in the SIR model
Lixin Lin1, Homayoun Hamedmoghadam2, Robert Shorten2
1Mathematical Sciences, School of Science, RMIT University, Melbourne, Australia.
Journal of the Royal Society, Interface
|September 17, 2024
Summary
Vaccination
Area of Science:
- Epidemiology
- Mathematical Modeling
- Public Health
Background:
- Vaccination campaigns exert direct and indirect effects on infectious disease spread.
- Indirect effects, where vaccinated individuals reduce transmission, benefit all but are challenging to quantify.
- Understanding these effects is crucial for effective public health strategies.
Purpose of the Study:
- To analytically calculate indirect vaccination effects using the susceptible-infected-recovered (SIR) model.
- To clarify the relationship between indirect effects and herd immunity.
- To distinguish between population-level and per capita indirect effects and analyze 'shielding' interventions.
Main Methods:
- Utilized the susceptible-infected-recovered (SIR) epidemiological model.
- Employed the final size formula for epidemics for analytical calculations.
- Incorporated 'shielding' strategies, including vaccination with imperfect efficacy.
Main Results:
- Provided analytical calculations for indirect vaccination effects in key scenarios.
- Demonstrated a significant difference between population-level and per capita indirect effects.
- Showcased how 'shielding' can be integrated with vaccination strategies.
Conclusions:
- Indirect vaccination effects are analytically calculable and distinct from herd immunity.
- Population-level and per capita indirect effects yield different conclusions.
- Mathematical modeling of 'shielding' and vaccination offers insights into disease control.
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