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

O. Osuna, J. G. Villavicencio Pulido

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.

Keywords


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

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References


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

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Trends in Computational and Applied Mathematics

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