DOI: http://dx.doi.org/10.18273/revint.v34n2-2016001

Osillations in seasonal SIR models with
saturated treatment

L. ROCÍO GONZÁLEZ-RAMÍREZ^{a, b}, OSVALDO OSUNA ^a*,
GEISER VILLAVICENCIO-PULIDO^c

^a Universidad Michoacana de San Nicolás de Hidalgo, Instituto de Física y
Matemáticas, Morelia, México.
^b Conacyt, D.F., México.
^c Universidad Autónoma Metropolitana Unidad Lerma, Departamento de Ciencias
Ambientales, Estado de México, México.

Abstract In this work, we give some conditions for the existen e of periodic orbits for a Susceptible-Infectious-Recovered (SIR) model with seasonal saturated incidence functions and saturated treatment rate. We use Leray-Schauder degree theory to prove the existence of periodic orbits.

Keywords: Leray-Schauder degree, SIR models, periodic orbits, reproductive number.
MSC2010: 37J45, 34C25, 92D30, 34D23.

Oscilaciones en modelos SIR estacionales con
tratamiento saturado

Resumen. En este trabajo presentamos condiciones suficientes para la existencia de soluciones periódicas en modelos epidemiológicos estacionales de tipo SIR con funciones de incidencia y de tratamiento saturados. Utilizamos la teoría de grado de Leray-Schauder para establecer la existencia de órbitas periódicas en tales modelos.

Palabras clave: Grado de Leray-Schauder, modelo SIR, órbitas periódicas, número reproductivo básico.

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^*E-mail: osvaldo@ifm.umich.mx
Received: 29 January 2016, Accepted: 11 May 2016.
To cite this article: L.R. González-Ramírez, O. Osuna, G. Villavicencio-Pulido, Oscillations in seasonal
SIR models with saturated treatment, Rev. Integr. Temas Mat. 34 (2016), No. 2, 125-131.