Abstract
This work aims to apply the SIR-type compartmental model (Susceptible - Infected - Removed) in the evolution of Covid-19 in Paraíba's State and Campina Grande City. For that, the parameters of the model were considered to be variable during time evolution, within an appropriate range. The system of differential equations was solved numerically using the Euler method. The parameters were obtained by adjusting the model to the infected data provided by the Paraíba Health Department. According to the results obtained, the model describes the infected population well. There was a reduction in the effective reproduction number in Paraíba and the town of Campina Grande. It is noteworthy that understanding the dynamics of infection transmission and evaluating the effectiveness of control measures is crucial to assess the potential for sustained transmission to occur in new areas. The model can also be applied to describe epidemic dynamics in other regions and countries.
Highlights
Several reports in history highlight the epidemics of diseases that have had dramatic effects on the population
As at the beginning of the Covid-19 epidemic, we did not have medicines and vaccines, we based ourselves on scenarios reported in the literature, considering different periods in which infected individuals remain in circulation, being able to transmit the virus to susceptible people, due to social distance measures
The initial parameters used are S(0) = 4, 010, 000 (estimated population of the Paraíba’s State by the Brazilian Institute of Geography and Statistics (IBGE)), R(0) = 1, and I(0) = 21, with 21 being the number of confirmed cases in Paraíba’s State in April 01, 2020. that it is reasonable to assume S(t)/N ≈ 1 at the beginning of the epidemic given that the number of recovered and deceased people as of April 01 should be, at most, of the same order as the number of infected people, which is negligible in respect to the total population
Summary
Several reports in history highlight the epidemics of diseases that have had dramatic effects on the population. The Spanish flu in 1918, caused by the influenza virus A H1N1 type, infected more than 500 million people and caused between 17 and 50 million deaths between 1918 and 1920 [1], [2]. Swine flu in 2009, the first pandemic of the 21st century, was caused by an extremely violent variation of the H1N1 virus. It originated in Mexico in March/April 2009 and spread to over 75 countries in 3 months and reaching over 120 countries. Other diseases have been reported, such as cholera, tuberculosis, smallpox, influenza, measles, and malaria, which have caused many deaths [3], [4]
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