Modelling infectious diseases with herd immunity in a randomly mixed population
Kian Boon Law1, Kalaiarasu M Peariasamy2, Hishamshah Mohd Ibrahim3
1Institute for Clinical Research, National Institutes of Health, Ministry of Health Malaysia, Setia Alam, Malaysia. kblaw@crc.gov.my.
Scientific Reports
|October 19, 2021
Summary
New SIR models improve infectious disease modeling by accounting for declining transmission rates, offering more accurate predictions for herd immunity and disease control compared to conventional methods.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Conventional susceptible-infectious-recovered (SIR) models may overestimate disease transmission and herd immunity thresholds.
- This can lead to inaccurate assessments of infection control and eradication needs.
Purpose of the Study:
- To develop and evaluate novel SIR frameworks that incorporate declining transmission rates.
- To overcome the limitations of conventional SIR models in predicting infectious disease dynamics and herd immunity.
Main Methods:
- Formulated two new SIR models (Model A and Model B) with declining transmission rates at different stages.
- Simulated infectious diseases with specific basic reproduction numbers (r0) and herd immunity thresholds (HIT), with and without vaccination.
- Compared model outcomes with the conventional SIR model and CDC estimates for seasonal influenza.
Main Results:
- Conventional SIR model overestimated infections, especially at higher population sizes and achieved HIT.
- Model A showed improved HIT attainment; Model B projected disease control at HIT only with high vaccination rates.
- Model B provided a credible framework for modeling infectious diseases with herd immunity in a randomly mixed population.
Conclusions:
- Allowing transmission rates to decline accurately models infectious disease dynamics with herd immunity.
- Novel SIR frameworks offer more precise predictions than conventional models, particularly for diseases with high r0 and low vaccination rates.
- Model B is recommended for modeling infectious diseases with herd immunity in randomly mixed populations.
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