2024/04/18 by Sonia Velasco, Velasco, Sonia · 1 citation
Biochemistry, Genetics and Molecular Biology · Neuroscience · #FOS: Mathematics #Genetic Neurodegenerative Diseases #Metabolism and Genetic Disorders #Mitochondrial Function and Pathology #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.2404.11963
openalex publication_date 2024/04/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce an interacting particle system which models the inherited sterility method. Individuals evolve on ℤd according to a contact process with parameter λ>0. With probability p ∈ [0,1] an offspring is fertile and can give birth to other individuals at rate λ. With probability 1-p, an offspring is sterile and blocks the site it sits on until it dies. The goal is to prove that at fixed λ, the system survives for large enough p and dies out for small enough p. The model is not attractive, since an increase of fertile individuals potentially causes that of sterile ones. However, thanks to a comparison argument with attractive models, we are able to answer our question.