![]() ![]() Still, it could be argued that this modified PSEIRD(S) model is overly complex for the description of the COVID-19 dynamics, but, as it will become evident in the following sections, it represents a balance between effective number of model parameters and an adequate description of this epidemic.įitting the solutions of differential equations is, undoubtedly, a non-trivial process and usually requires an extensive overhead work to implement dedicated software. ![]() The PSEIRD(S) model was modified in order to account for vaccination and avoiding infectious pathways that required the use of parameters which could not be independently estimated, such as the fraction of infected individuals that, regardless of being detected, do not infect others. 11 to fit the data sets related to the infected, deceased and hospitalized cases reported for Portugal, a country that had a severe post-Christmas outbreak. Here we propose a model based on the comprehensive PSEIRD(S) model by Beira et al. The number of daily new cases, deceased and recovered related to COVID-19 is made available to the general public in close to real time 16, 17, which makes it possible to test models by actually fitting the existing data. Probably, this is the main reason why only a very limited number of scientific works actually provide the fit of the SIR-type model differential equations systems to the COVID-19 related data 6, 7, 11 and why others prefer to fit the data using approximated analytical expressions, such as the logistic function 14, 15. These compartmental SIR-models are composed of systems of differential equations that, except for a few particular cases, have no analytical solutions 13. McKendrick 3, published in 1927, on the compartmental SIR model, have paved the way for epidemiologists to mathematically describe the dynamics of infectious diseases and became increasingly popular among the scientific community, particularly for the analysis of the current pandemic 4, 5, 6, 7, 8, 9, 10, 11, 12. Furthermore, this happened despite what might be considered the largest lock-down in history. COVID-19, caused by SARS-CoV-2 (Severe Acute Respiratory Syndrome CoronaVirus 2), is, however, the first pandemic to ever reach every country in the world within this era of global information. Infectious diseases have accompanied mankind since the beginning of its existence and are known to have profoundly influenced the fate of entire nations upon their evolution to local epidemics or to great pandemics 2. ![]() The method presented in this work can easily be used to perform the non-trivial task of simultaneously fitting differential equation solutions to different epidemiological data sets, regardless of the model or country that might be considered in the analysis.īack on January 2020, when the World Health Organization (WHO) first mentioned a cluster of pneumonia cases in Wuhan, no one expected that by the 11th of March, COVID-19 (COronaVIrus Disease-19) would have spread across the globe and would be declared a pandemic 1. This analysis enabled the data-driven validation of the used model and was the basis for robust projections of different future scenarios, namely, increasing the detected infected population, reopening schools at different moments, allowing Easter celebrations to take place and population vaccination. Taking advantage of the real-time availability of COVID-19 related data, we perform a compartmental model fitting analysis of the portuguese case, using an online open-access platform with the integrated capability of solving systems of differential equations. It is, therefore, not surprising that they are frequently used to study the current COVID-19 pandemic. Compartmental epidemiological models are, by far, the most popular in the study of dynamics related with infectious diseases. ![]()
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