Logistic Sigmoidal and Neural Network Modeling for COVID-19 Death Waves

The rapid spread of the pandemic of the coronavirus disease 2019 (COVID-19) has caused enormous problems and many deaths. Therefore, it is essential to construct epidemiological models for forecasting and prevention. The main objective of this study is to develop a novel model F(x), treating the cumulative number of deaths due to COVID-19 using two approaches: the logistic sigmoidal function and an artificial neural network. In addition, to estimate models for the death rate F ′ (x). The research is longitudinal. Data were downloaded from Johns Hopkins University for four countries. It is shown that the logistic function is efficient within the basic sigmoidal functions, and a new variant of the function is obtained and used. The contribution of this work is the model that can be used on data that are not necessarily epidemiological and with any function, where, as x approaches positive and negative infinity, the function tends to a constant value. Also, the method of its construction and the calculation of high-order derivatives allow for the development of a practical model, as well as justification of the term “Wave(s)”. The turning points (i.e., the place where the concavity changes) are also obtained and confirmed. Finally, they were applied to real-world datasets. The sigmoidal models yielded better fits than previous works with Pearson correlation coefficients of 0.99992 in Italy, 0.99993 in Brazil, 0.99992 in Switzerland, and 0.99991 in Peru; on the other hand, the Neural Networks reported root mean square errors of 0.0252, 0.0176, 0.0226, and 0.0132, respectively. The models are representative and predictive; they are helpful to understand the pandemic and improve future public health responses.