Analysis of covid-19 outbreak in ecuador using the logistic model

Abstract

At the end of 2019, the COVID-19 disease emerged in the city of Wuhan, China, and caused an outbreak of unusual viral pneumonia. Being highly transmissible, this novel coronavirus disease has spread fast all over the world. COVID-19 continues to challenge most developed countries in the search for an effective strategy to either prevent infection or to avoid the spreading of the disease. While several developed countries have managed to contain COVID-19, several countries in Latin America continue to report an increase in the daily number of infected people. Ecuador, particularly, became the epicenter of the COVID-19 outbreak in the region during March and April 2020. In this context, the present study shows a simple mathematical approach to understand the effect of the COVID-19 outbreak in Ecuador (and some Latin American countries such as Brazil, Peru, and Colombia). The proposed method is based on the exponential model, discrete logistic equation, and differential logistic model using one-year data from March 1, 2020, to February 28, 2021. This study presents the estimated growth rate coefficient (λ), the total number of cases (N), and the midpoint of maximum infection (t_0) as well as the variability of the λ coefficient as a function of total cases and time. The exponential model shows a high value of λ=0.185 which decreases to λ=0.014 and λ=0.056 according to the discrete and differential logistic models, respectively. An accurate value of the total number of cases of infected people was found by analyzing the number of daily cases as a function of the total of cases whose value (N~409 K) agrees with the data reported at the end of May 2021, validating the proposed approach. How to use the current mathematical approach for long-term prediction is also discussed here. Most importantly, the proposed method has two important characteristics: (i) the mathematical model is as simple as possible compared to other time-consuming approaches, and (ii) it can be used to study the effect of COVID-19 and predicts its consequences in other countries, allowing revenue new decisions against the COVID-19 disease.