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Coronavirus disease (Covid-19) caused millions of confirmed cases and deaths worldwide since first appeared in China. Forecasting methods are essential to take precautions early and control the spread of this rapidly expanding pandemic. Therefore, in this research, a new customized hybrid model consisting of Back Propagation-Based Artificial Neural Network (BP-ANN), Correlated Additive Model (CAM) and Auto-Regressive Integrated Moving Average (ARIMA) models were developed for the purpose of forecast Covid-19 prevalence in Brazil, US, Russia and India. The Covid-19 dataset is obtained from the World Health Organization website from 22 January, 2020 to 6 January, 2021. Various parameters were tested to select the best ARIMA models for these countries based on the lowest MAPE values (5.21, 11.42, 1.45, 2.72) for Brazil, the US, Russia and India, respectively. On the other hand, the proposed BP-ANN model itself provided less satisfactory MAPE values. Finally, the developed new customized hybrid model was achieved to obtain the best MAPE results (4.69, 6.4, 0.63, 2.25) for forecasting Covid-19 prevalence in Brazil, the US, Russia and India, respectively. Those results emphasize the validity of our hybrid model. Besides, the proposed prediction models can assist countries in terms of taking important precautions to control the spread of Covid-19 in the world. [ABSTRACT FROM AUTHOR]