Modelagem matemática da evolução da pandemia de covid-19 no Brasil

Abstract

After the emergence of a new infectious disease, caused by the SARS-COV-2 coronavirus, the world’s medical authorities realized its rapid contagion, significant mortality rate and potential risk for the collapse of Health Systems worldwide. Thus in March 2020, the World Health Organization (WHO) declared a worldwide pandemic of the disease COVID-19, caused by this virus. Decision-making by authorities in times of health crisis, such as those caused by COVID-19, requires strict actions to interrupt the contagion cycle, for example restricting contact between people from different family groups. On the other hand, one must be aware of the impacts of these measures on affected societies, especially in the productive and educational sectors, balancing the harmful effects of these measures as well as the disease itself. One of the tools to help managers make decisions is mathematical modeling with epidemiology models to simulate different scenarios. These tools allow for a more balanced and grounded analysis of the potential impacts of their decisions on the epidemic. In this work, after a study of different models, an adaptation of the SIR model was made. This model describes the dynamics between susceptible, infected and removed individuals, so as to simulate the development of the pandemic in Brazil. When solving the inverse problem, functions were adjusted to reflect the transmission and lethality rates, according to the adapted model. These numbers could then be compared to the official data on cases and deaths provided by the Ministry of Health. In the simulations carried out, he noted the influence of these rates (which are directly influenced by the control measures) on the contagion and death curves caused by the disease is considerable. The importance of immunizing the population through administering vaccines is one of the most expressive results observed in the simulations. This suggests that with the advance of vaccination, it was possible to loosen social isolation rules, and consequently resume economic, social and educational activities, without a significant rise in the contagion and death curves. Thus, the data obtained in the model corroborate the actual situation experienced in Brazil, confirming that mass vaccination is one of the most effective ways to control an epidemic, together with other measures adopted that directly impact the transmission rate, such as social isolation, use of masks and reinforcement of hygiene habits in general.