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The deterministic limit of infectious disease models with dynamic partners
1Division of Health Computer Sciences, University of Minnesota, Minneapolis 55455, USA. michael@umnhcs.labmed.umn.edu
Mathematical Biosciences
|July 10, 1998
Summary
This study models infectious disease spread in large populations through partnerships. It constructs a deterministic system and compares approximations, finding accuracy depends on epidemic stage and partnership duration.
Area of Science:
- Epidemiology
- Mathematical Biology
- Network Science
Background:
- Infectious disease dynamics are complex, influenced by contact patterns.
- Previous stochastic models analyzed key epidemiological parameters.
- Understanding large population dynamics requires deterministic approximations.
Purpose of the Study:
- To construct the deterministic limit of an infectious disease model with concurrent partnerships.
- To analyze the accuracy of existing approximations for this model.
- To generalize the model for dependencies among partnerships.
Main Methods:
- Development of a deterministic system from a stochastic model using two scaling factors.
- Comparison of a Watts and May approximation with the exact solution.
- Generalization of the model to incorporate arbitrary distributions of partnership numbers.
Main Results:
- A novel construction of the deterministic system for large populations was achieved.
- The Watts and May approximation shows highest accuracy early in epidemics and with short partnerships.
- The generalized model accommodates proportional mixing with diverse partnership structures.
Conclusions:
- The deterministic model provides a framework for analyzing large-scale infectious disease spread via partnerships.
- Approximation accuracy is context-dependent, highlighting the need for precise modeling.
- The generalized model offers flexibility for studying various contact network structures in disease transmission.