Source-Sink Dynamics in a Two-Patch SI Epidemic Model with Life Stages and No Recovery from Infection.
Jimmy Calvo-Monge1, Jorge Arroyo-Esquivel2, Alyssa Gehman3
1Escuela de Matemática, Universidad de Costa Rica, San Pedro, San José, 11501, Costa Rica.
Bulletin of Mathematical Biology
|July 8, 2024
Summary
Ecological rescue is possible for endangered populations through disease management and maintaining healthy source populations. Juvenile dispersal and maturation rates are key to population recovery and conservation efforts.
Area of Science:
- Ecology
- Epidemiology
- Mathematical Biology
Background:
- Emerging infectious diseases threaten natural populations, exemplified by amphibian chytridiomycosis and Sea Star Wasting Disease.
- Host-pathogen dynamics in spatially structured environments are complex and require further investigation for effective conservation.
Purpose of the Study:
- To analyze a two-patch, two-life stage SI model to understand ecological rescue dynamics.
- To identify conditions for a healthier source population to rescue a diseased sink population.
Main Methods:
- Mathematical and numerical analysis of a Susceptible-Infected (SI) model without recovery.
- Investigation of parameters including basic reproductive numbers, maturation rate, and juvenile dispersal rate.
Main Results:
- Identified critical roles of source and sink population reproductive numbers, maturation, and dispersal rates in population outcomes.
- Determined conditions for a receiving patch to achieve population recovery through rescue effects.
Conclusions:
- Maintaining reproductively viable refuge populations is crucial for conservation.
- Dispersal and maturation rates significantly impact population recovery from disease.
- Multi-faceted conservation strategies are needed to address biodiversity loss due to emerging diseases.
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