On restricting the infected population peak of a SIR modeled epidemic by a reduced interventionDUCED INTERVENTION

MARTÍN IGNACIO ERRÁZQUIN; GRACIELA ADRIANA GONZÁLEZ

Río de Jnaeiro

Congreso; Latin American Congress on Industrial and Applied Mathematics; 2023

Sociedad Brasilera de Matemática Aplicada

The well known SIR model is one of the simplest but efficient epidemiological models. Itis determined by a set of differential equations which represent the dynamics of the susceptible,infected and recovered population groups. These dynamics depend on the parameters β (infectionrate) and γ (mean recovery rate). The disease outbreak closely hinges on R0 = β/γ, knownas the reproduction number.If R0 is too large, a great proportion of the susceptible population becomes infected yieldingto an undesirable peak of the infected population. This peak may be reduced by implementinga set of actions, referred to as ?non-pharmaceutical intervention? (NPI) . The SIR-with-NPI can be modeled by introducing q(t), the fraction of contact prevented through interventionwhich varies between 0 and 1. Increasing the value of q is equivalent to decreasing β and hence,reducing the peak of the crisis.This effect is colloquially known as ?flattening the curve? which persists as long as theintervention is held on. A premature relax or removal of the intervention, that is, to make qtake values near or equal to zero early, may yield to a second outbreak. On the other hand,holding restrictions for a long term results unviable. This work aims to identify strategies q forcontrolling the peak of the infected population curve by means of a reduced intervention.Nota: El archivo adjunto contiene el resumen que fue aceptado. El trabajo completo se presentará en formato poster (en preparación).