Traditionally, endemic diseases such as dengue, diarrhea, and tuberculosis are modeled separately, which leads to a limited understanding of current disease dynamics and an inaccurate evaluation of the parameters of the different models. In this study, we propose a joint spatiotemporal model to predict the risks of multiple endemic diseases and identify hotspots. The model includes spatial shared component random effects and a covariate for healthy behavior. The model was applied to the joint modeling of dengue, diarrhea, and tuberculosis in thirty districts in Bandung, Indonesia over a five-year period. Our findings show that the joint model was effective in understanding the characteristics of the diseases. One potential advantage of using shared component models is that they can identify diseases with spatial or temporal distribution patterns and consider shared risk factors that may be spatially correlated, such as climate. It is recommended to conduct exploratory analyses to determine the correlation between the risks of the diseases being studied and the reference disease before using this type of model.

Deep learning techniques are making significant contributions to the rapid advancements in forecasting. A standout algorithm known for its ability to produce accurate forecasts by recognizing temporal autocorrelation within the data is the Long Short-Term Memory (LSTM) algorithm, a component of Recurrent Neural Networks (RNN). The LSTM method employs both stateless and stateful architecture approaches, providing versatility in its application. This research aims to compare stateful and stateless algorithms in LSTM models, focusing on forecasting stock prices, such as those of Apple Inc. This comparative analysis is crucial, taking into account various characteristics of time series data, including the benefits and drawbacks of temporal autocorrelation. The comparison results reveal that, despite the stateful algorithm requiring more computational time, it achieves greater accuracy than the stateless approach. The forecast indicates a potential upward trend in share prices for the period of January to December 2024, according to the projected outlook for Apple's stock value. However, it is essential to exercise prudence in interpreting these results, considering that share price fluctuations are influenced by a significant number of variables.

The main objectives of this research are to identify significant spatial and temporal components associated with diarrhea and provide an accurate forecast. Using data from the Ban-dung city health surveillance system, the analysis reveals a decreasing trend in both the number of incidences and the estimated relative risks of diarrhea in most districts. Key factors contributing to diarrhea variation include temporally structured, spatially structured, and unstructured effects of space-time interaction Type I. No clear seasonal pattern is observed in diarrhea incidence among children under five, emphasizing the need for consistent vigilance and preventive measures. Spatial clustering was observed in the eastern and western parts of Bandung city. The forecasting model predicts a continued decline in diarrhea incidence and relative risk throughout 2022.