Chemostats and epidemics: competition for nutrients/hosts.

Area of Science:

• Ecology
• Epidemiology
• Mathematical Biology

Background:

• Chemostat models predict competitive exclusion based on lowest break-even concentration.
• Epidemic models predict pathogen strain dominance using the basic reproduction number.
• Both models involve competition for a single resource or host population.

Purpose of the Study:

• To compare and contrast winner prediction in chemostat and epidemic competition models.
• To investigate the conditions under which different prediction metrics are accurate.
• To extend competition theory to include global outcomes and nonproportional functional responses.

Main Methods:

• Comparative analysis of mathematical models for chemostat and epidemic competition.
• Derivation of conditions for equivalence and divergence of prediction metrics.
• Inclusion of global stability analysis for nonproportional functional responses.

Main Results:

• Chemostat and epidemic models yield the same winner prediction only if functional responses are proportional.
• When functional responses are nonproportional, break-even concentration accurately predicts the winner.
• A new class of models incorporating global competition outcomes was developed for nonproportional responses.

Conclusions:

• Break-even concentration is a more robust predictor of competitive success than the basic reproduction number in certain ecological and epidemiological scenarios.
• The assumption of proportional functional responses is critical for the equivalence of standard prediction metrics.
• Future research should consider global competition dynamics and non-autonomous models for a comprehensive understanding of ecological and epidemiological outcomes.