Long memory in reservoirs for dengue forecasting with scarce data

The prediction of infectious diseases such as dengue represents a major technical challenge for public health systems. Incidence time series are usually short, noisy, non-stationary and have a long-range temporal dependence that classical statistical models fail to capture adequately. In this context, the combination of artificial intelligence and reservoir computation techniques has emerged as a promising alternative, especially when available data is scarce. This article discusses the fundamentals of long memory models in reservoirs, their application to dengue forecasting, and how companies can implement these solutions using specialized technology services. In a scenario where predictive power can save lives, understanding the right tools makes all the difference. Traditional methods such as ARFIMA (fractionally integrated autoregressive moving average model) offer a balance between non-stationarity and persistence, but their linear structure limits the capture of nonlinear dynamics. Deep neural networks, on the other hand, model complex patterns, but they require large volumes of training data and do not explicitly incorporate long-term memory. This is where Echo State Networks (ESNs) within the reservoir computing paradigm offer a middle way: they retain nonlinear recurring dynamics while training only a simple read layer, making them ideal for contexts with limited data. However, standard ESNs lack long-term memory mechanisms from a time series perspective. To overcome this limitation, recent research proposes a long-memory reservoir computing framework that integrates two types of reservoirs: one dedicated to long-term memory and the other to short-term memory, combined using a Ridge regression. Two variants stand out: Fractional ESN (fESN), which incorporates fractional differentiation dynamics directly into the reservoir to encode long-range dependence, and Wavelet ESN (wESN), which extracts stable low-frequency components using wavelet smoothing before modeling them with a memory-conscious reservoir. Both variants have been shown to outperform statistical and deep learning models across multiple dengue datasets and forecast horizons. In addition, when combined with conformal prediction, calibrated and distribution-free uncertainty intervals are generated. The practical relevance of these models goes beyond the academic field. For a technology company like Q2BSTUDIO, the development of custom applications that incorporate artificial intelligence for companies, such as these forecasting systems, can transform health management. Imagine a system that, fed with historical data on cases, temperature, humidity and mobility, generates early warnings weeks in advance. AI agents can monitor predictions in real time and activate prevention protocols, while business intelligence service tools such as Power BI visualize risk maps for decision-makers. The correct implementation of these models also requires a robust infrastructure. AWS and Azure cloud services offer the scalability needed to process large volumes of data and run complex simulations without upfront investment in hardware. On the other hand, cybersecurity is crucial when handling sensitive health data; pentesting audits ensure that the platform complies with regulations such as GDPR or HIPAA. From a technical perspective, the success of reservoirs with long memory lies in the ability to generate temporal dependence with polynomial decay, mimicking the behavior of processes with statistical long memory. This is in contrast to standard ESNs, which under mild conditions induce short memory processes. The design of these reservoirs is not trivial; It involves careful selection of connection weights and activation function. In practice, the Q2BSTUDIO team can help organizations implement these architectures using enterprise AI solutions, tailoring reservoir parameters to the specific characteristics of each dataset. In addition, process automation allows models to be updated periodically without manual intervention, reducing operating costs. The long-memory approach also has applications in other sectors, such as finance, climatology or logistics, where time series have similar properties. The ability to work with scarce data without sacrificing accuracy is especially valuable in emerging markets where historical records are limited. Companies that adopt these technologies gain a significant competitive advantage. As a final thought, dengue forecasting is just one example of how the combination of artificial intelligence, custom software, and cloud services can address complex problems with limited resources. Collaboration with software development specialists ensures that the solutions are not only technically sound, but also scalable, secure, and aligned with business objectives.