Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 300, pp. 1-10.
Periodic orbits for seasonal SIRS models with non-linear incidence rates
Laura Rocio Gonzalez-Ramirez, Osvaldo Osuna, Ruben Santaella-Forero
Abstract:
In this work, we prove the existence of periodic solutions
for a seasonally-dependent SIRS model using Leray-Schauder degree theory.
We obtain criteria for the uniqueness and asymptotic stability of the
periodic solution of the system. We also present suitable examples of
a seasonal epidemiological disease.
Submitted July 10, 2015. Published December 7, 2015.
Math Subject Classifications: 342C5, 37J45, 92D30.
Key Words: Leray-Schauder degree; SIRS models; periodic orbits.
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Laura Rocio González-Ramírez
Instituto de Física y Matemáticas
Universidad Michoacana de san Nicolás de Hidalgo
Edif. C-3, Cd. Universitaria, C.P. 58040
Morelia, Mich., México
email: rgonzalez@ifm.umich.mx
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Osvaldo Osuna
Instituto de Física y Matemáticas
Universidad Michoacana de san Nicolás de Hidalgo
Edif. C-3, Cd. Universitaria, C.P. 58040
Morelia, Mich., México
email: osvaldo@ifm.umich.mx
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Ruben Santaella-Forero
Instituto de Física y Matemáticas
Universidad Michoacana de san Nicolás de Hidalgo
Edif. C-3, Cd. Universitaria, C.P. 58040
Morelia, Mich., México
email: rusanfo@matmor.unam.mx
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