A Consistent Discrete Version of a Nonautonomous SIRVS Model

• Autor(a) principal: Mateus, Joaquim
• Data de Publicação: 2018
• Outros Autores: Silva, César, Vaz, Sandra
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10314/4076; https://doi.org/Joaquim Mateus, César M. Silva, and S. Vaz, “A Consistent Discrete Version of a Nonautonomous SIRVS Model,” Discrete Dynamics in Nature and Society, vol. 2018, Article ID 8152032, 18 pages, 2018. https://doi.org/10.1155/2018/8152032.
• topic: Epidemic model; Non-autonomous; Global stability; numerical method

A family of discrete nonautonomous SIRVS models with general incidence is obtained from a continuous family of models by applyingMickens nonstandard discretizationmethod. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. Concerning extinction and persistence, the consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (permanence) for the continuous model, we also have extinction (permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data.