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Characterizing the next-generation matrix and basic reproduction number in ecological epidemiology
M G Roberts1, J A P Heesterbeek
1Institute of Information and Mathematical Sciences, New Zealand Institute for Advanced Study, and Infectious Disease Research Centre, Massey University, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand. m.g.roberts@massey.ac.nz
Journal of Mathematical Biology
|October 23, 2012
Summary
This study models how infectious diseases interact with ecological processes in host-non-host communities. The research extends the next-generation matrix approach to calculate the basic reproduction number (R₀), linking ecological and epidemiological dynamics.
Area of Science:
- Ecology
- Epidemiology
- Mathematical Biology
Background:
- Understanding infectious disease dynamics in ecosystems requires integrating ecological processes like consumer-resource relationships and competition.
- Host-pathogen interactions within multi-species communities are complex and influence disease spread and ecological stability.
Purpose of the Study:
- To develop a modeling framework that links ecological community structure with infectious disease epidemiology.
- To extend the next-generation matrix method for calculating the basic reproduction number (R₀) in multi-host systems.
- To explore how ecological interactions are mediated by pathogens and their impact on species coexistence.
Main Methods:
- Extension of the epidemiological next-generation matrix approach to incorporate ecological community matrices.
- Calculation of the basic reproduction number (R₀) within an integrated ecological-epidemiological framework.
- Application of the model to two case studies: rinderpest-wildebeest-grass dynamics and a predator-prey system with a shared pathogen.
Main Results:
- The model successfully captures qualitative dynamics observed after rinderpest eradication in the Serengeti.
- In a predator-prey system, the pathogen's presence can mediate ecological interactions, enabling host species coexistence.
- The study demonstrates a quantitative link between ecological community structure and disease invasion potential (R₀).
Conclusions:
- Integrating ecological and epidemiological models provides essential insights into infectious agent dynamics in complex communities.
- The extended next-generation matrix approach offers a robust method for analyzing host-pathogen systems.
- Pathogen-mediated interactions can be crucial for maintaining biodiversity and community stability.
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