Quarantine in an epidemic model with seasonality

  • Carmen CollEmail author
  • Elena Sánchez
Original Paper


In this work, we focus on the periodicity of recurrent epidemic patterns and propose a periodic model that includes quarantine as a control strategy. So, we consider that susceptible individuals can be quarantined (Q) and then return to the recovered class once it is determined that they are not infected. We use the basic reproductive number \({\mathcal {R}}_0\) to analyze the spread of the disease. To study the effectiveness of quarantine in the spread of the disease, a new parameter \({\mathcal {R}}_q\) is introduced. This is defined as the average number of new infections that a case generates, in a totally susceptible population when quarantine is applied to individuals during the time they are infectious. The value of \({\mathcal {R}}_q\) will be closely related to both the intensity of the intervention and the severity of the epidemic in the absence of such intervention. The behavior in absence of control will be determined by the value of the basic reproductive number \({\mathcal {R}}_0\).


Quarantine Periodic model Epidemic model Basic reproductive number 

Mathematics Subject Classification

92D30 93C55 93D20 



This work is supported by Spanish Grant MTM2013-43678-P.


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Copyright information

© The Royal Academy of Sciences, Madrid 2019

Authors and Affiliations

  1. 1.Institut Universitari de Matemàtica MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain

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