An SEIQR model for childhood diseases
David J Gerberry1, Fabio A Milner
1Department of Mathematics, Purdue University, West Lafayette, IN 47907-2067, USA. gerberry@math.purdue.edu
Journal of Mathematical Biology
|December 11, 2008
Summary
Adding a latent class to the SIR model explains recurrent childhood disease outbreaks. This deterministic model closely matches scarlet fever data, suggesting isolation is not the primary driver for other diseases.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Dynamics
Background:
- Classical SIR models suggest isolated individuals can cause disease oscillations.
- Recurrent outbreaks may stem from autonomous, deterministic factors.
Purpose of the Study:
- Extend the SIR model to include a latent class.
- Analyze the dynamics of childhood infectious diseases with a latent period.
- Investigate the role of latent infection in disease recurrence.
Main Methods:
- Mathematical modeling using the SIR model with an added latent class.
- Analysis of model dynamics, including Hopf and homoclinic bifurcations.
- Comparison of model predictions with historical epidemiological data for scarlet fever.
Main Results:
- The extended SIR model with a latent class demonstrates self-sustained oscillations.
- Hopf bifurcations and homoclinic bifurcations were identified in the model.
- The model incorporating a latent class showed significantly better agreement with scarlet fever data than the classical SIR model.
Conclusions:
- A latent class in the SIR model can explain recurrent childhood disease outbreaks through deterministic factors.
- The model provides a closer fit to scarlet fever epidemiological data.
- For other childhood diseases, isolation is less likely to be the main driver of sustained oscillations.
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