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Species coexistence and periodicity in host-host-pathogen models
Herbert W Hethcote1, Wendi Wang, Yi Li
1Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, 52242, USA. herbert-hethcote@uiowa.edu
Journal of Mathematical Biology
|June 9, 2005
Summary
This study reveals that frequency-dependent incidence models for infectious disease transmission exhibit classic endemic behavior, unlike mass-action models which show complex dynamics. This highlights significant differences in disease modeling approaches.
Area of Science:
- Epidemiology
- Mathematical Biology
- Infectious Disease Dynamics
Background:
- Previous infectious disease models using mass-action incidence exhibit complex behaviors like multiple equilibria and periodic solutions.
- Understanding disease transmission dynamics is crucial for public health interventions.
Purpose of the Study:
- To analyze infectious disease transmission models in one and two host populations.
- To compare the behaviors of models using mass-action incidence versus frequency-dependent incidence.
Main Methods:
- Formulation and analysis of mathematical models for infectious disease transmission.
- Comparison of model dynamics based on different incidence formulations (mass-action vs. frequency-dependent).
Main Results:
- Models with frequency-dependent incidence demonstrate classic endemic behavior: disease dies out below a threshold and persists above it.
- In contrast, mass-action incidence models can display unusual dynamics, including multiple positive equilibria and periodic solutions.
- The study reinforces that incidence formulation significantly impacts model behavior.
Conclusions:
- Frequency-dependent incidence provides a more predictable and classic endemic model behavior.
- Mass-action incidence can lead to complex and less intuitive disease dynamics.
- The choice of incidence function is critical in accurately modeling infectious disease transmission.