Mathematical approach of the SIR epidemiological model for the comprehension of the containment measures against the Covid-19

Abstract

In December 2019, an acute respiratory disease outbreak from zoonotic origin was detected in the city of Wuhan, China. The outbreak’s infectious agent was a type of coronavirus never seen. Thenceforth, the Covid-19 disease has rapidly spread to more than 200 countries around the world. To minimize the devastating effects of the virus, the States have adopted epidemiological measures of various kinds that involved enormous economic expenses and the massive use of the media to explain the measures to the entire population. For the prediction and mitigation of infectious events, various epidemiological models, such as SIR, SEIR, MSIR and MSEIR, are used. Among them, the most widely used is the SIR model, which is based on the analysis of the transition of individuals susceptible to infection (S) to the state of infected individuals that infect (I) and, finally, to that of recovered (cured or deceased) (R), by using differential equations. The objective of this article was the mathematical development of the SIR model and its application to predict the course of the Covid-19 pandemic in the city of Santa Marta (Colombia), in order to understand the reason behind several of the measures of containment adopted by the States of the world in the fight against the pandemic.