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A baseline model for the apparent competition between many host strains: the evolution of host resistance to
1Department of Mathematical Sciences, The University of Liverpool, M&O Building, Liverpool, L69 3BX, U.K. sx04@liv.ac.uk
Abstract:
The purpose of this article is to establish and analyse a baseline model for the apparent competition between many host strains attempting to avoid a uniform microparasitic population. The model is formulated and analysed using invasion criteria in the main text. The results are verified by more formal methods in the appendix. Cases in which the microparasite can invade are distinguished geometrically from those in which it cannot using threshold and strain composition conditions. A major result obtained when the pathogen persists is a competitive exclusion principle for host resistance. For non-lethal infections, the winning strain is that which affords the pathogen maximum threshold density; for possibly lethal infections, a somewhat generalized version of this criterion is presented and discussed. The tension is highlighted between these results and the baseline behaviour of many pathogen strains and a uniform host population-here the winning pathogen strain is that with minimum threshold density.
Insights
This study models host-pathogen competition, revealing a competitive exclusion principle for host resistance. The optimal host strain depends on infection lethality, balancing pathogen invasion and host survival.
Area of Science:
- Evolutionary biology
- Mathematical modeling
- Epidemiology
Background:
- Understanding host-pathogen dynamics is crucial for predicting disease spread and evolution.
- Host populations often exhibit genetic diversity, influencing their susceptibility to pathogens.
- Microparasitic infections present complex evolutionary challenges for host populations.
Purpose of the Study:
- To establish and analyze a baseline mathematical model for host-pathogen competition.
- To investigate the interplay between multiple host strains and a uniform microparasitic population.
- To identify conditions governing pathogen invasion and host resistance evolution.
Main Methods:
- Formulation and analysis of a mathematical model using invasion criteria.
- Geometric distinction of pathogen invasion scenarios based on threshold and strain composition.
- Verification of results using formal mathematical methods in an appendix.
Main Results:
- A competitive exclusion principle for host resistance emerges when the pathogen persists.
- For non-lethal infections, the optimal host strain maximizes pathogen threshold density.
- A generalized criterion for potentially lethal infections is presented, contrasting with uniform host populations.
Conclusions:
- Host resistance strategies are shaped by the pathogen's invasion capabilities and infection severity.
- The model highlights a tension between diverse host populations and uniform pathogen behavior.
- Understanding these evolutionary trade-offs is key to managing infectious diseases.