# American Institute of Mathematical Sciences

## Random perturbations of an eco-epidemiological model

 1 Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, and Instituto Superior de Ciências da Educação, Rua Sarmento Rodrigues, Lubango, Angola 2 Centro de Matemática e Aplicações (CMA-UBI), Universidade da Beira Interior, Rua Marquês d'Ávila e Bolama, 6201-001, Covilhã, Portugal

* Corresponding author: Helder Vilarinho

Received  September 2020 Revised  December 2020 Published  January 2021

Fund Project: L. F. de Jesus, C. M. Silva and H. Vilarinho were partially supported by FCT through CMA-UBI (project UIDB/MAT/00212/2020). L. F. de Jesus was also supported by INAGBE

We consider random perturbations of a general eco-epidemiological model. We prove the existence of a global random attractor, the persistence of susceptibles preys and provide conditions for the simultaneous extinction of infectives and predators. We also discuss the dynamics of the corresponding random epidemiological $SI$ and predator-prey models. We obtain for this cases a global random attractor, prove the prevalence of susceptibles/preys and provide conditions for the extinctions of infectives/predators.

Citation: Lopo F. de Jesus, César M. Silva, Helder Vilarinho. Random perturbations of an eco-epidemiological model. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2021040
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