Quarantine in an Epidemic Model with Seasonality

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 \({\mathcal {R}}_0\).