Existence of periodic solutions of a periodic SEIRS model with general incidence.

• Autor(a) principal: Mateus, Joaquim
• Data de Publicação: 2017
• Outros Autores: Silva, César
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10314/3946; https://doi.org/doi.org/10.1016/j.nonrwa.2016.09.013
• topic: Epidemic model Periodic Stability

For a family of periodic SEIRS models with general incidence, we prove the existence of at least one endemic periodic orbit when some condition related to R0 holds. Additionally, we prove the existence of a unique disease-free periodic orbit, that is globally asymptotically stable when R0 < 1. In particular, our main result generalizes the one in Zhang et al. (2012). We also discuss some examples where our results apply and show that, in some particular situations, we have a sharp threshold between existence and non existence of an endemic periodic orbit.