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Many types of research have been carried out with the aim of combating the COVID-19 pandemic since the first outbreak was detected in Wuhan, China. Anticipating the evolution of an outbreak helps to devise suitable economic, social and health care strategies to mitigate the effects of the virus. For this reason, predicting the SARS-CoV-2 transmission rate has become one of the most important and challenging problems of the past months. In this paper, we apply a two-stage mid and long-term forecasting framework to the epidemic situation in eight districts of Andalusia, Spain. First, an analytical procedure is performed iteratively to fit polynomial curves to the cumulative curve of contagions. Then, the extracted information is used for estimating the parameters and structure of an evolutionary artificial neural network with hybrid architectures (i.e., with different basis functions for the hidden nodes) while considering single and simultaneous time horizon estimations. The results obtained demonstrate that including polynomial information extracted during the training stage significantly improves the mid- and long-term estimations in seven of the eight considered districts. The increase in average accuracy (for the joint mid- and long-term horizon forecasts) is 37.61% and 35.53% when considering the single and simultaneous forecast approaches, respectively. • Estimated polynomial model coefficients serve as COVID19 contagion rate descriptors. • EANNs are used to build valid predictors for different pandemic stages. • Considering curve polynomial descriptors significantly improve the model performances. • Simultaneous Multi-Task EANN forecast perform better in Málaga with simpler models. [ABSTRACT FROM AUTHOR]