Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence

Authors

  • O. Osuna
  • J. G. Villavicencio Pulido Universidad Autónoma Metropolitana

DOI:

https://doi.org/10.5540/tcam.2021.022.02.00279

Keywords:

Seasonal treatment rate, periodic orbit, Leray-Schauder degree, SIRS models, reproduction number

Abstract

We analyze a seasonal $SIR$ model that assumes a periodic treatment rate. Using the Leray-Schauder degree theory, we prove that model shows periodic solutions. This result shows that sustained oscillations in the incidence of the disease are related to the periodic application of a treatment against the disease. So, we can say that the periodic application of treatment can be considered a seasonal driver of the sustained oscillations.

Author Biography

J. G. Villavicencio Pulido, Universidad Autónoma Metropolitana

Departamento de Ciencias Ambientales.

Profesor-Titular C.

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Published

2021-06-28

How to Cite

Osuna, O., & Villavicencio Pulido, J. G. (2021). Seasonal Treatment of an Infectious Disease is a Social Driver of Sustained Oscillations in the Disease incidence. Trends in Computational and Applied Mathematics, 22(2), 279–289. https://doi.org/10.5540/tcam.2021.022.02.00279

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Section

Original Article