Competing species models with an infectious disease
Roberto A Saenz1, Herbert W Hethcote
1Applied Mathematical and Computational Sciences, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242. roberto-saenz@uiowa.edu.
Mathematical Biosciences and Engineering : MBE
|April 6, 2010
Summary
Infectious diseases in competing species either die out or persist in both populations. A modified reproduction number (R(1)) determines if the disease is eliminated or becomes endemic, impacting species competition outcomes.
Area of Science:
- Mathematical biology
- Epidemiology
- Ecology
Background:
- Infectious diseases can influence the dynamics of competing species.
- Understanding disease transmission in multi-species systems is crucial for ecological predictions.
Purpose of the Study:
- To analyze the impact of frequency-dependent disease incidence on competing species dynamics.
- To determine the conditions under which a disease persists or is eliminated in a multi-species context.
Main Methods:
- Utilized mathematical modeling, specifically SIS, SIR, and SIRS models.
- Employed global analysis and introduced a modified reproduction number (R(1)) to predict disease outcomes.
Main Results:
- The modified reproduction number (R(1)) dictates disease extinction (R(1) <= 1) or endemic persistence (R(1)) > 1).
- Disease-altered birth and death rates can shift the competitive balance between species.
- A critical finding is that the disease uniformly affects both species, either dying out or becoming endemic in both.
Conclusions:
- Frequency-dependent disease incidence in competing species leads to a coupled disease dynamic: it's either absent in both or present in both.
- The outcome of interspecific competition can be significantly altered by the presence of a shared infectious disease.
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