Fig 1.
(a) Distribution of confirmed Monkeypox cases across the studied nations, (b) Geographical representation of the studied nations on a global map.
Fig 2.
(a) Sequence of confirmed MPXV instances in Canada, with a detailed view of the peak interval (June to October 2022), (b) Sequence of confirmed MPXV instances in Portugal, with a detailed view of the peak interval (June to October 2022), (c) Sequence of confirmed MPXV instances in Spain, with a detailed view of the peak interval (June to October 2022), (d) Sequence of confirmed MPXV instances in the USA, with a detailed view of the peak interval (June to October 2022).
Fig 3.
Flowchart of the 10-fold cross-validation process.
Fig 4.
Flowchart depicting the 10-fold cross-validation process used in neural network model training and evaluation.
Fig 5.
Iteration-dependent evolution of the ANN model’s training performance for MPXV, evaluated using the mean squared error (MSE) metric.
Fig 6.
Iteration-dependent evolution of the LSTM model’s training performance for MPXV, evaluated using the mean squared error (MSE) metric.
Fig 7.
Iteration-dependent evolution of the GRU model’s training performance for MPXV, evaluated using the mean squared error (MSE) metric.
Fig 8.
Learning curves for ANN models across four different countries: Canada, Portugal, Spain, and the United States.
The training process is represented by the blue line and the validation process by the red line, with the reduction in loss over epochs indicating effective learning.
Fig 9.
Learning curves for LSTM models in Canada, Portugal, Spain, and the United States.
Each subplot shows the training loss (blue line) decreasing over epochs, indicative of the model’s learning capacity, while the validation loss (red line) presents fluctuations, reflecting the model’s generalization to new data. Notable is the slight convergence between the two losses, suggesting a balance between learning and model complexity.
Fig 10.
Learning curves for GRU models across Canada, Portugal, Spain, and the United States, displaying the evolution of model training and validation losses.
The blue line indicates the training loss, which decreases with epochs, signifying learning, while the red line denotes the validation loss, showing fluctuations that point to the challenges in model generalization. The convergence of training and validation losses is particularly evident for Canada and the United States, suggesting a more effective model fit.
Table 1.
Identification of the most suitable ANN configuration with a single hidden layer for the Canada dataset.
Table 2.
Determination of the best ANN configuration with two hidden layers for the Canada dataset.
Table 3.
Identification of the most suitable LSTM configuration with a single hidden layer for the Canada dataset.
Table 4.
Determination of the best LSTM configuration with two hidden layers for the Canada dataset.
Table 5.
Identification of the most suitable GRU configuration with a single hidden layer for the Canada dataset.
Table 6.
Determination of the best GRU configuration with two hidden layers for the Canada dataset.
Table 7.
Identification of the most suitable ANN configuration with a single hidden layer for the Portugal dataset.
Table 8.
Determination of the best ANN configuration with two hidden layers for the Portugal dataset.
Table 9.
Identification of the most suitable LSTM configuration with a single hidden layer for the Portugal dataset.
Table 10.
Determination of the best LSTM configuration with two hidden layers for the Portugal dataset.
Table 11.
Identification of the most suitable GRU configuration with a single hidden layer for the Portugal dataset.
Table 12.
Determination of the best GRU configuration with two hidden layers for the Portugal dataset.
Table 13.
Identification of the most suitable ANN configuration with a single hidden layer for the Spain dataset.
Table 14.
Determination of the best ANN configuration with two hidden layers for the Spain dataset.
Table 15.
Identification of the most suitable LSTM configuration with a single hidden layer for the Spain dataset.
Table 16.
Determination of the best LSTM configuration with two hidden layers for the Spain dataset.
Table 17.
Identification of the most suitable GRU configuration with a single hidden layer for the Spain dataset.
Table 18.
Determination of the best GRU configuration with two hidden layers for the Spain dataset.
Table 19.
Identification of the most suitable ANN configuration with a single hidden layer for the USA dataset.
Table 20.
Determination of the best ANN configuration with two hidden layers for the USA dataset.
Table 21.
Identification of the most suitable LSTM configuration with a single hidden layer for the USA dataset.
Table 22.
Determination of the best LSTM configuration with two hidden layers for the USA dataset.
Table 23.
Identification of the most suitable GRU configuration with a single hidden layer for the USA dataset.
Table 24.
Determination of the best GRU configuration with two hidden layers for the USA dataset.
Table 25.
Comprehensive performance of best models across datasets.
Table 26.
Forecasting comparisons across countries.