Soft Computing of a Medically Important Arthropod Vector with Autoregressive Recurrent and Focused Time Delay Artificial Neural Networks

Abstract

A central issue of public health strategies is the availability of decision tools to be used in the preventive management of the transmission cycle of vector-borne diseases. In this work, we present, for the first time, a soft system computing modeling approach using two dynamic artificial neural network (ANNs) models to describe and predict the non-linear incidence and time evolution of a medically important mosquito species, Culex sp., in Northern Greece. The first model is an exogenous non-linear autoregressive recurrent neural network (NARX), which is designed to take as inputs the temperature as an exogenous variable and mosquito abundance as endogenous variable. The second model is a focused time-delay neural network (FTD), which takes into account only the temperature variable as input to provide forecasts of the mosquito abundance as the target variable. Both models behaved well considering the non-linear nature of the adult mosquito abundance data. Although, the NARX model predicted slightly better (R = 0.623) compared to the FTD model (R = 0.534), the advantage of the FTD over the NARX neural network model is that it can be applied in the case where past values of the population system, here mosquito abundance, are not available for their forecasting.

Keywords: Culex sp.; FTD model; NARX model; decision making; mosquito population system; public health.

Figure 1

Graphical illustration of the NARX network with du input and dy output memory and a number of neurons in the hidden layer. Note that if the output memory is set at dy = 0, then the NARX network is reduced to a plain FTD neural network architecture.

Figure 2

Abbreviated dynamic model structure, in a parallel mode, of the overall NARX network for the input layer (a) and the output layer (b), according to the Mat Lab Simulink ANN system model construction process (details in text).

Figure 3

NARX (a) and FTD (b) neural network training, validation, and testing performance. Note that the best validation performance for the NARX model was 0.388 at epoch 3, and for the FDR model, it was 0.276 at epoch 3.

Figure 4

NARX (a) and FTD (b) neural network training, validation, and testing performance. Note that the best validation performance for the NARX model was 0.388 at epoch 3, and for the FDR model, it was 0.276 at epoch 3.

Figure 5

Response of the NARX (a) and FTD (b) neural network model output to the mosquito population time series and error. The model training was performed in an open loop (i.e., parallel series architecture), including the validation and testing step, and later on, after training, it was transformed to a closed loop for the multistep-ahead prediction.

Figure 6

Error histogram chart having 20 bins for the NARX (a) and the FTD (b) neural network.

Figure 7

Autocorrelation values of the NARX (a) and the FTD (b) model in respect to different time lags and related confidence limits.

Figure 7

Autocorrelation values of the NARX (a) and the FTD (b) model in respect to different time lags and related confidence limits.

Figure 8

Graphical illustration of the logical operations followed to develop the dynamics autoregressive ANNs models for predicting adult mosquito population dynamics (left). Real-time data can be used later to forecast the arthropod vector population dynamics based on the calibrated ANN model that has been developed or to be retrained under new circumstances (right).