Patient and public involvement

No patient involved.

Data collection and data preprocessing

We collected monthly malaria cases in all 31 provinces in China from January 2004 to December 2016. The data set contains four classes of Plasmodium species that is P. falciparum, P. vivax, P. malariae and other Plasmodium species. The plasmodium species category named other could be P.ovale, P. knowlesi or unidentified species type. Malaria cases for all 31 provinces of mainland China were obtained from the Chinese Center for Disease Control and Prevention (www.phsciencedata.cn)27 which provides the database for infectious diseases. The meteorological data of these 31 provinces were obtained from the China Meteorological data service centre (http://data.cma.cn/en).28 A total of 10 meteorological variables (ie, pressure, average temperature, maximum temperature, wind speed, minimum temperature, wind direction, precipitation, average relative humidity, sunshine duration, minimum relative humidity) were retained with no missing values in all features of meteorological data. To prevent overfitting while training the deep learning models, we used feature selection to remove redundant attributes. We reduced some of the meteorological variables using high correlation filtering and low variance filtering. Four variables (ie, pressure, wind speed, wind direction, sunshine duration) were discarded as they had the smallest variance in all the study areas. In total, 10 valid features (ie, six meteorological features and four types of malaria parasites) were considered in our study as shown in figure 1.

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Figure 1

Guangdong climatic variables and P. falciparum used to train models. ARH, Average Relative Humidity; Avt, Average Temperature; MaxT, Maximum Temperature; MinT, Minimum Temperature; MRH, Minimum Relative Humidity; P. falciparum, Plasmodium falciparum.

Train-validation-test split

To train and evaluate the machine learning and neural network frameworks proposed in this paper, we divided the data set into the train, validation and test sets. In our experiment, 70% of the whole data set was used to train the model. We have allocated 15% of the data set for validation. The validation set was used to evaluate the model after each training epoch and ensure that the model is not overfitting the training data set. After the model has finished training, the remaining 15% of the data set was used to evaluate the model as the test set. The data was not shuffled before splitting to ensure that the validation set and test set results are more realistic. We allocated the period 1 January 2004 to 31 December 2012 to the training set and the period 1 January 2013 to 31 December 2014 is allocated to the validation set. The remaining period is allocated for the testing set.

Prediction models

This study proposes a sequence-to-sequence (Seq2Seq) prediction model based on the LSTM neural networks. The model will be used to forecast the re-emergence of malaria cases by considering the influence of meteorological factors on malaria cases in all 31 provinces of China. We compared the performance of our constructed LSTMSeq2Seq recurrent neural networks with other machine learning and deep neural networks prediction models, including XGBoost (extreme gradient boosting), GRU network and LSTM network models. Here is a brief description of our proposed Seq2Seq model as well as other employed models. These models achieved the best performance for predicting, diagnosing and controlling infectious diseases.

XGBoost model

The XGBoost is an ensemble machine learning algorithm that is flexible and easy to interpret. It provides an efficient implementation of gradient boosting machine learning model thought to be competent in the healthcare industry. A significant number of studies in public health have applied the XGBoost based framework to exploit data sources and predict infectious diseases such as dengue fever. The XGBoost model can achieve incredible performance in predicting vector-borne infectious diseases such as dengue or those caused by the West Nile virus.29 It has been used for forecasting, prevention and early diagnosis of infectious diseases30 31 and non-communicable diseases.32 The hyperparameters in this gradient boosting model were tuned to optimise the XGBoost model and achieve the best performance in our study. After testing several XGBoost parameters and the number of time steps as inputs, we chose 100 trees as the number of estimators to avoid overfitting. We used the GridSearchCV method in scikit-learn to tuning the hyperparameter and a learning rate of 0.8 and a maximum depth of 8. This method greatly reduces the prediction error of our XGBoost model. We used the defined types of monthly observation plasmodium incidence (P. falciparum, P. vivax, P. malariae and another class named other in our experiments) and climatic variables such as maximum temperature, average temperature, minimum temperature, average relative humidity, minimum relative humidity and rainfall to train the XGBoost approach and evaluate its performance on the test data set.

LSTM model

An LSTM describes a long short-term memory neural network and belongs to a class of recurrent neural networks (RNNs). RNN can process current data by using the previous data. It has effectively been used to solve problems of sequential time series such as climate modelling, web traffic prediction, financial prediction, neuroscience, intrusion detection, anomaly detection, air quality forecasting, medical monitoring. Meanwhile, RNN suffers from gradient vanishing and exploding problems when processing long-term dependencies sequences. The LSTM was developed as an intelligent recurrent neural network to specifically address the gradient vanishing problem by relying on memory cells, which have self-connections that store network temporal state, and are controlled by a set of three gates: input, output and forget. These gates and the memory cell can record information for a long time, thereby solving the problem of long-term dependencies and can predict the next time feature, which implies that it can forecast the next time step conditional on the previous values of the times series. LSTM’s ability to successfully learn from data with long-range temporal dependencies makes it a natural choice for time-series predictions. This model has achieved superior performance in predicting vector-borne infectious diseases like dengue fever33 and is one of the potential deep learning predictive models for childhood infectious diseases. It recently has been applied as one of the state-of-the-art deep neural networks in forecasting COVID-19.34–36 We developed a two-layer LSTM model that includes 128 and 32 memory cells and uses a batch size of 32 and a diagnostic of 1000 epochs. It consists of seven input parameters for each of the four classes of Plasmodium species, that is, P. falciparum. We have the monthly observation of P. falciparum incidences, maximum temperature, average temperature, minimum temperature, average relative humidity, minimum relative humidity and rainfall as the input vector sequence of the same month.

GRU model

GRU is an improved recurrent neural network as a simple variant of LSTM by combining the input gate and forgetting gate into a single gate called update gate. GRU comprises of update gate and resets gate, and it can only control information inside the unit because it has no additional memory cell to keep information. Researchers have applied this framework to forecast infectious diseases such as influenza.37 For the GRU model, we used the same hyperparameters as for LSTM models. The training data set was created using 12 months as input to our GRU model and the next month as output. The same input vector sequence as shown in figure 1 consists of seven input parameters for each of the four classes of Plasmodium species and six climatic variables. The six climatic variables, maximum temperature, average temperature, minimum temperature, average relative humidity, minimum relative humidity and rainfall, have been trained on the GRU model and used to test its performance.

LSTMSeq2Seq model

There are intuitively two different tasks to predict time series: understanding what has happened by looking at the known values of the past and predicting what will happen in the future. These two tasks require two different skill sets. The first is the ability to look at the past values and create an idea of the state of the system in the present. The second is the ability to use that understanding of the current state in the system to predict how the system will evolve in the future. As we mentioned earlier, LSTM predicts the next time feature, which implies that it can forecast the attribute of the next time step of input only. When we used a single LSTM cell in our model, we asked it to be capable of remembering both main events of the past and using those events to predict future values. Unlike single LSTM, we can use a Seq2Seq model with two specialised LSTM cells capable of predicting multiple time steps rather than having a single multitasking cell. Seq2Seq refers to the sequence-to-sequence architecture of the neural network fit. This architecture enables mapping between sequences of arbitrary length. As a result, Seq2Seq can perform many tasks, including language translation, image captioning and time series prediction. The Seq2Seq architecture is made up of an encoder and a decoder, as illustrated in figure 2.

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Figure 2

Long short-term memory (LSTM) sequence-to-sequence architecture.

LSTMSeq2Seq model consists of two major blocks: encoder LSTM cell and decoder LSTM cell. The encoder outputs the encoder vector as input to the decoder block. The decoder encodes the input vector and predicts the next time step output. Subsequently, if X_t is the input of the next feature sequence, then the LSTM sequence model outputs Xt_t+1 as the next time step feature.

The following are the formula for the encoder and decoder networks.

(1)

where H^E_t represents the current hidden state at time step t, W^HE is the appropriate weight of the old hidden state at time step t-1 and W^x represents the appropriate weight to the input vector X_t .

Equation (1) shows the result of a general sequence of the ordinary recurrent neural networks with the formula for the encoder. It is only necessary to apply an appropriate weight to the previous hidden state H^E_t−1 and the input vector X_t.

(2)

where H^D_t is the current decoder hidden state, we are just using the old hidden state of the input vector at some time step t-1 to compute the next one and f is some function of the parameter.

Equation (2) is a stack of numerous recurrences that forecast each output y_t at time t as a formula for the decoder. Each reiteration unit accepts a hidden state from the old unit and generates its hidden state.

The output y_t at time step t is computed using the formula (3).

(3)

y_t is the final output state at time step t computed using softmax (is used to create a probability vector which will help us determine the final output) function and its respective weight W^s.

Equation (3) calculates the output using the state hidden at the current time step with each weight W^S.

We designed an encoder that looks back into 12 months of historical data and a decoder that slide 6 months to predict, we have used t+12 months as input to the decoder as illustrated in figure 2 of our designed LSTMSeq2Seq model, the t+12 time step which is the encoder vector was used as input to the decoder and LSTM decoder cell predicts the next six steps ahead from t+1 to t+6 of malaria incidence. Apart from dropout, L1 regularisation and L2 regularisation were employed to avoid overfitting by preventing the weights of each network from being too high in the GRU, LSTM and LSTMSeq2Seq models. Each layer’s high parameter values can cause the network to concentrate severely on a few features, which can lead to overfitting. Weight regularisation added a cost to the loss function of the network for large weights. As a result, the models were forced to learn only the relevant patterns in the training data.

Model validation

Using two metrics loss function scores, we evaluated the performances of our methods for predicting the re-emergence of malaria incidence based on meteorological factors. First, we used RMSE as the basis for evaluating continuous variables by measuring the average differences between predicted and observed error values.

(4)

where y_t is the Plasmodium cases of observation for time t, and ŷ_t is the number of cases predicted by the model. A lower RMSE value indicates that there is a slight difference between the predicted Plasmodium cases and observed ones and implicates a high prediction accuracy of the model. Second, we used mean absolute error (MAE) to assess numerically the prediction error of the sequence and calculate the average value of the errors between Plasmodium cases of observation for the current time step and the predicted cases.

(5)