The COVID-19 pandemic has exposed the fragility of healthcare systems, especially in the management of Intensive Care Unit (ICU) resources. Accurate forecasting of ICU occupancy is essential to support public health decisions and to prevent saturation during epidemic waves. In this work, we propose a predictive model based on Long Short-Term Memory (LSTM) neural networks, combined with Monte Carlo dropout to estimate model uncertainty. This approach allows us to generate probabilistic forecasts of ICU demand, including confidence intervals that help quantify prediction reliability. We apply the model to real-world data from California counties, using historical ICU occupancy records collected during the pandemic. We show that the model can anticipate trends up to several weeks in advance, maintaining good accuracy and consistent uncertainty calibration. To assess robustness, we compare the proposed LSTM model with simpler architectures, including GRU-based and feedforward neural networks, confirming the superior performance of LSTM in capturing complex temporal patterns. Our results highlight the importance of integrating uncertainty estimates into forecasting systems, particularly in high-risk domains such as healthcare. The method is computationally eficient, easy to implement, and adaptable to other time series prediction tasks where uncertainty awareness is required.
ration, while excessively conservative estimates can lead Several studies have explored the application of
mato the waste of precious resources [
To address this, we adopt the concept of model un- missions, ICU transfers, and mortality risk. These
apcertainty as formulated by Gal and Ghahramani [
In this work, we apply this methodology to a Long Cheng et al. [
We test this approach on real-world data concerning to build a risk score for ICU admission and patient morICU occupancy across counties in California during the tality. Their model showed good performance, especially COVID-19 pandemic, with the goal of providing a flex- in identifying the most relevant clinical predictors. ible and interpretable forecasting system. The results Beyond direct ICU prediction, many authors have proindicate that the model is able to provide meaningful posed machine learning systems designed to detect early forecasts, even several weeks in advance, and that the warning signals and support preventive decision-making. uncertainty estimation can serve as a key element in the For instance, studies during the COVID-19 pandemic process of healthcare planning. In addition to evaluating have explored how to integrate clinical markers with psyprediction accuracy, we also assess the calibration of the chological, behavioral, and societal factors. A growing uncertainty estimates, that is, how well the predicted number of works has highlighted the potential of comconfidence intervals match the true variability of future bining multimodal data, including physiological signals data. and high-level cognitive features, to support healthcare
In the following sections, we will review related works response strategies. (Section 2), present the theoretical foundations of LSTM Notable eforts have also focused on the detection networks and model uncertainty (Section 3.1), describe and classification of disinformation related to COVID-19, our proposed model in detail (Section 4), report on exper- which may indirectly afect the behavior of the popuimental results and model performance (Section 5), and lation and the load on hospital systems. De Magistris ifnally discuss the implications, limitations, and future et al. [26] proposed an explainable fake news detection directions of our research (Section 6). system combining named entity recognition and stance classification, showing that misinformation during a pandemic can propagate uncertainty and reduce adherence 2. Related Works to preventive measures, thus indirectly afecting hospital saturation patterns.
The prediction of ICU occupancy during health emer- Complementary studies explored the psychological gencies, such as the COVID-19 pandemic, has received and neurocognitive consequences of the pandemic, esincreasing attention from the scientific community. This pecially in relation to post-COVID stress syndromes. In interest is motivated by the urgent need to support health- particular, Russo et al. [27] proposed an innovative apcare systems in optimizing the use of limited resources, proach using remote EMDR therapy to treat long-COVIDespecially in times of crisis. related traumatic disorders. Such works are relevant be
cause they reveal how the pandemic impacted not only physical but also psychological health, both of which can influence the demand on healthcare facilities. In this section we present the main theoretical founda
From a methodological point of view, advanced clus- tions upon which our work is built. The aim is to provide tering and statistical learning techniques have been used the conceptual and methodological background needed to analyze both behavioral data and physiological signals to understand the structure and rationale of the model we in the context of pandemic-related stress. For example, propose. Forecasting ICU occupancy during a pandemic Ponzi et al. [28] used Expectation Maximization and presents a unique combination of challenges: on one Gaussian Mixture Models to investigate the diferences hand, the system evolves over time in a non-linear and in psychodiagnostic profiles before and after the pan- context-dependent way; on the other hand, any predicdemic, using Rorschach test data. These types of investi- tive model must be able to represent and communicate its gations, though not focused directly on ICU occupancy, own uncertainty to support decision-making processes enrich the broader understanding of pandemic impacts in high-risk environments. on healthcare systems. To address these requirements, our work is based on
Moreover, the use of computer vision methods for two fundamental components. The first is the use of surveillance and prevention has seen widespread exper- Long Short-Term Memory (LSTM) networks, a class of imentation. De Magistris et al. [29] developed an auto- recurrent neural networks specifically designed to promatic CNN-based system for face mask detection, tested cess sequential data. LSTMs are particularly well suited in real-world scenarios during the COVID-19 emergency. to time series forecasting tasks where past values influMonitoring compliance with mask-wearing policies is ence future observations, even across long temporal gaps. another aspect that, indirectly, afects the spread of in- Their internal structure allows them to capture dependenfection and therefore the load on ICU infrastructures. cies over time more efectively than traditional models,
While these models and applications provide impor- making them ideal for modeling ICU admission patterns, tant insights, most of them focus on patient-level pre- which often follow delayed and seasonally modulated diction using static clinical data, or address secondary trends. aspects related to prevention and communication. In The second key component is the use of Monte Carlo contrast, our approach focuses on a population-level pre- dropout, a technique that allows us to estimate the prediction of ICU bed usage, considering temporal dynam- dictive uncertainty of deep learning models in a comics and variability over time. This aspect is crucial in a putationally eficient way. Instead of relying on fully pandemic, where the number of new infections and hos- Bayesian neural networks, which are dificult to implepitalizations can change rapidly due to social behavior, ment and often computationally prohibitive, Monte Carlo public policies, and virus mutations. dropout enables approximate Bayesian inference through
The closest works to our approach are the studies stochastic forward passes in standard architectures. This
by Gal and Ghahramani [
Therefore, our work builds upon these contributions subsections describe each component in detail. by integrating the dropout-as-Bayesian approach with LSTM networks for time series forecasting. This combi- 3.1. Long Short-Term Memory (LSTM) nation enables us to provide not only accurate predictions Networks of ICU occupancy, but also to associate each prediction with a quantitative measure of uncertainty. This feature LSTM networks are a special type of Recurrent Neuis fundamental in supporting cautious and informed de- ral Networks (RNNs), specifically designed to handle cisions in critical contexts such as healthcare planning sequences and temporal dependencies. Traditional RNNs during a pandemic. sufer from problems such as the vanishing or exploding gradient, which make it dificult to learn long-term dependencies in time series. LSTMs solve this limitation by introducing a more sophisticated memory unit that includes several internal gates: the input gate, the forget
gate, and the output gate [
Each LSTM cell contains a memory unit that can main- bed usage but also to associate each prediction with a tain information over long periods of time. The input confidence interval. This is particularly useful in guiding gate controls how much new information is stored, the decisions regarding the allocation of resources, where the forget gate decides what information to discard, and the cost of a false prediction can be extremely high. Using output gate determines how much of the memory is ex- dropout in this way enables a form of Bayesian modeling posed to the next layers of the network. This internal that is computationally eficient and compatible with mechanism allows LSTMs to learn long-range patterns modern deep learning frameworks. and to keep important signals in memory while ignoring irrelevant data.
Due to these characteristics, LSTM networks are 4. Proposed Model widely used in many real-world applications involving sequential data, such as speech recognition, financial forecasting, and medical monitoring [30]. In our study, we use a multi-layer LSTM network to model the temporal evolution of ICU occupancy in diferent regions, allowing the system to capture the non-linear dependencies and seasonalities typical of epidemic curves.
model based on Long Short-Term Memory (LSTM) networks, enhanced with a method to quantify uncertainty using Monte Carlo dropout. The goal is to build a predictive system that can provide both the expected number of ICU beds occupied in the near future and the associated confidence intervals. This dual output is essential to support decision-makers in high-risk and high-variability environments such as healthcare. (1) (2)
estimates: they predict a single value for each input. However, in high-stakes contexts like healthcare, it is essential not only to predict a value, but also to know how confident the model is in its prediction. This concept is known as model uncertainty.
A promising method to estimate uncertainty in neural
networks is the technique proposed by Gal and
Ghahramani [
In practice, this approach is implemented using Monte Carlo dropout (MC dropout). During inference, multiple stochastic forward passes are executed through the same network with dropout activated, and the results are averaged. This procedure generates both the expected output and a measure of variance, which reflects the model’s confidence. Formally, if we perform forward passes, each with a diferent dropout mask, the predictive mean is estimated as: and the predictive variance as:
E[* ] =
1 ∑︁ ˆ* () =1 V[* ] =
1 ∑︁ ˆ* 2() − (E[* ])2 =1
During the pandemic, the evolution of ICU occupancy followed complex temporal patterns. These patterns are not only influenced by biological and medical factors (e.g., virus spread, severity of cases), but also by non-linear external factors such as lockdown policies, vaccination campaigns, or population movements. To capture these dynamics, it is necessary to adopt a model that is able to learn temporal dependencies and nonlinearities from past sequences.
Moreover, the data used for such predictions are subject to noise, inconsistencies, and rapid changes in trends. Hence, our model must also be able to express its own uncertainty: this means providing not only a prediction, but also an estimate of how reliable that prediction is. A decision made on a forecast with high uncertainty should be treated diferently than one based on a highly confident output.
current layers, each followed by a dropout layer. The use of stacked LSTM layers allows the model to learn increasingly abstract temporal patterns, while the dropout layers serve both as regularization (during training) and as a Bayesian approximation (during inference).
Each model takes as input a univariate time series representing the number of ICU patients at time . Optionally, an encoded representation of the county is also included if multiple counties are modeled together. The model outputs a prediction ˆ+1, i.e., the estimated
number of ICU beds that will be occupied in the next counties) either separately or jointly using encoded
identime step. tifiers; it provides interpretable uncertainty estimates
without requiring a full probabilistic model or
compu4.3. Dropout in Recurrent Layers tationally expensive Bayesian methods; it is compatible
with any modern deep learning framework and can be
The novelty of our approach is in the use of **recur- deployed on standard hardware.
rent dropout** with fixed masks, as proposed by Gal In the next section, we describe the experimental
proand Ghahramani [
During training, dropout is applied both to input and recurrent connections. The same is done during inference, which transforms the deterministic prediction into a stochastic one. Each forward pass through the network generates a slightly diferent result, depending on the random dropout masks.
ical framework that interprets dropout as an approximation of Bayesian inference. This idea, introduced by Gal and Ghahramani, allows us to treat standard neural networks as approximate Bayesian models, without requiring changes in the model architecture or complex probabilistic methods.
In classical Bayesian inference, the goal is to estimate the posterior distribution of the model parameters given the observed data. Formally, we aim to compute:
dropout method. Specifically, we perform stochastic forward passes at test time, each time using a diferent dropout mask. This process yields a set of predictions {ˆ(+1)1, ˆ(+2)1, . . . , ˆ(+ )1}.
From this set, we compute: • The predictive mean: • The predictive variance: ¯+1 =
1 ∑︁ ˆ+1
() =1 V[+1] =
1 ∑︁ (︁ =1
() )︁ 2 ˆ+1 − (¯+1)2 ( | ) = ( | ) · ( ) ()
(3) where represents the weights of the model and is the training dataset. However, this posterior is typically intractable in neural networks, due to the high dimensionality of the parameter space and the non-linear nature of the model.
To overcome this dicfiulty, variational inference can be used. The idea is to approximate the true posterior distribution ( | ) with a simpler distribution ( ), and to find the parameters of that minimize the Kullback-Leibler divergence between and the true posterior. This is equivalent to maximizing the evidence lower bound (ELBO), defined as:
These statistics allow us to construct prediction intervals at various confidence levels (e.g., 68%, 95%, 99%). The In the interpretation proposed by Gal, the application wider the interval, the higher the uncertainty. This is of dropout during training and inference corresponds to especially important for hospital administrators: a sharp sampling from a variational distribution ( ), where increase in uncertainty may signal unusual trends, re- the weights are randomly masked by a binary matrix quiring increased attention or human intervention. drawn from a Bernoulli distribution. Specifically, each weight matrix is redefined as: ℒ = E( )[log ( | )] −
KL(( )‖( )) (4)
= · diag(), ∼
(5)
a regularization method, but as a way to simulate multiple network configurations drawn from the approximate posterior distribution. Each stochastic forward pass corresponds to a sample from the variational approximation.
The predictive distribution for a new input * is ob- 5.2. Time Series Preprocessing tained by marginalizing over the weight distribution: (* | * , ) = ∫︁ (* | * , ) · ( ) (6)
is estimated by Monte Carlo sampling. In practice, we perform multiple forward passes through the network using diferent dropout masks and compute the empirical mean and variance of the predictions: E[* ] ≈
1 ∑︁ ˆ* , =1
Var[* ] ≈
1 ∑︁ (ˆ* )2− (E[* ])2 =1
Since our objective is to predict ICU occupancy over time, we treated each county’s record as a univariate time series. The raw data are noisy and afected by local fluctuations (e.g., reporting delays, corrections). Therefore, we applied the following preprocessing steps:
1. Missing Data Handling: Missing values were interpolated using a linear method, as long as the proportion of missing points was below 10% in a time series.
Counties with too many missing values were excluded.
2. Normalization: To make the training process more stable, we scaled the data. Two scaling strategies were used: Standard Scaler: applied to grouped counties (mean 0, standard deviation 1); MinMax Scaler: applied to singlecounty models, with upper bound equal to the mean ICU occupancy mean (rather than 1), to reduce saturation efects.
3. Sliding Window: To generate training sequences, we applied a sliding window of fixed size = 14 days.
Each input sample is a sequence of ICU values over 14 days, and the target is the ICU value on the 15th day.
(7)
This approach makes it possible to estimate the epistemic uncertainty of the model without requiring the use of fully Bayesian neural networks, which are often dificult to implement and computationally expensive.
In summary, the Bayesian interpretation of dropout provides a principled way to incorporate model uncertainty into deep learning. This is particularly important in healthcare applications, where decisions based on pre- 5.3. Grouping Similar Counties dictions must also take into account the confidence in those predictions. By applying Monte Carlo dropout, To avoid building a separate model for each county, we our model can ofer both the expected evolution of ICU explored the possibility of grouping counties with similar occupancy and a reliable measure of its own uncertainty. ICU occupancy profiles. We applied the Dynamic Time Warping (DTW) algorithm to compute pairwise distances between the normalized time series. Counties with low 5. Experiments DTW distance were grouped together, resulting in six distinct clusters.
In this section, we describe the experimental framework This grouping reduces the number of models to be used to validate our approach. We first present the dataset trained. and improves model generalization by sharing and the criteria adopted for its selection. Then we ex- statistical patterns across counties with similar epidemic plain the preprocessing operations necessary to train the curves. model. Finally, we report the training strategies and the performance metrics used to evaluate both accuracy and 5.4. Dropout Rate Tuning uncertainty.
5.1. Dataset Description ability in the range [0.05, 0.3]. We observed that lower dropout rates (e.g., = 0.08) yield more stable predicWe used an open-access dataset provided by the Cali- tions, especially when training on small datasets. Higher fornia Department of Public Health (CDPH) [31]. The dropout values resulted in wider uncertainty bands, but dataset includes daily data on the COVID-19 pandemic sometimes degraded the mean prediction. collected at the county level, covering the period from This analysis confirmed the need to carefully tune March 2020 to May 2021. Specifically, we focused on the dropout rates when using MC dropout for uncertainty number of ICU beds occupied by confirmed COVID-19 estimation. patients in each county.
The dataset includes measurements for 58 counties. 5.5. Monte Carlo Estimation However, not all of them have complete or stable records.
To ensure data reliability, we performed a quality control At test time, we performed = 1000 stochastic forward phase and excluded counties with excessive missing val- passes through the trained model. For each input winues or inconsistent time series. The final dataset included dow, we obtained the predictive mean ¯ as the average 36 counties, which represent a good balance between geographic coverage and data quality.
with = 1, 1.96, 2.58
Square Error (RMSE): to assess the accuracy of point forecasts ⎯
RMSE = ⎷⎸⎸ 1 ∑︁( − ˆ)2 =1 Moreover we also used Calibration of Uncertainty as the percentage of true values falling within the predicted 95% confidence interval.
Across all counties, the average RMSE was 1.7 on the training set and 3.0 on the test set, confirming the model’s ability to generalize across time.
These results demonstrate the model’s ability to produce reliable and interpretable forecasts, even several weeks ahead. The use of uncertainty estimates increases trustworthiness and allows for more cautious resource planning.
To better assess the efectiveness of the proposed LSTMbased model with Monte Carlo dropout, we conducted a comparative study with two alternative neural architectures. The objective was to evaluate the importance of temporal memory, recurrent structure, and uncertainty estimation by analyzing models with diferent levels of complexity and expressiveness. 5.7.1. GRU-based model 95% C.I. 94.1% 91.3% 88.6% Model LSTM + MC Dropout GRU + MC Dropout Feedforward + MC Dropout 5.7.2. Feedforward model with sliding window
work with no recurrent connections. The input to the network was a fixed-size sliding window of the previous 14 days of ICU occupancy, and the output was the prediction for the following day.
This model was also trained with dropout, and uncertainty estimation was performed using Monte Carlo sampling. Despite its simplicity, the feedforward model performed reasonably well on counties with very regular trends. However, it failed to capture long-term dependencies and reacted poorly to abrupt changes, such as second-wave peaks. 5.7.3. Performance comparison
models in terms of Root Mean Square Error (RMSE) and confidence interval calibration, defined as the percentage of true values falling within the 95% confidence band.
The results show that the LSTM model achieves the best accuracy and the most reliable uncertainty quantification. The GRU model ofers a good trade-of between speed and precision, but sufers slightly in unstable or noisy series. The feedforward model is clearly less capable in capturing temporal patterns, but still provides reasonable performance in regular conditions.
These findings support the adoption of LSTM networks when forecasting complex time series in healthcare contexts, especially when the time horizon is long and the dynamics are non-linear. While simpler models may be suficient for low-variability environments, they do not generalize well to unseen epidemic behaviors.
In addition, the LSTM model showed more stable uncertainty calibration, with narrower but better-aligned confidence intervals. This is important in critical settings, where over- or under-confidence of outputs, the standard deviation as a measure of un- Table 1 certainty, and the confidence intervals at 68%, 95%, and Comparison of model performance 99% using standard Gaussian quantiles:
LSTM networks. They have fewer parameters and use only two gates: an update gate and a reset gate. The reduced complexity makes GRUs faster to train, especially when computational resources are limited. 6. Conclusion
In our experiments, we implemented a GRU model with the same structure as the LSTM model (four recur- The work presented in this article proposes a forecastrent layers), applying Monte Carlo dropout in the same ing method for ICU occupancy based on a combination way. The performance was slightly lower than the LSTM of recurrent neural networks and approximate Bayesian model, particularly in time series with strong seasonality inference techniques. By integrating Long Short-Term or abrupt changes. However, training time was reduced Memory (LSTM) models with Monte Carlo dropout, we by approximately 30%. were able to develop a system that does not limit itself to generating single-point predictions, but also estimates healthcare systems more resilient. In scenarios characthe uncertainty associated with each forecast. This ap- terized by volatility and risk, the ability to predict with proach represents a step forward in the context of health- caution and to quantify doubt becomes just as important care, where decision-making often takes place under time as the ability to predict with precision. pressure, with incomplete information and high social responsibility.
Through the analysis of data collected in California 7. Declaration on Generative AI during the COVID-19 pandemic, we observed that the proposed model is capable of maintaining stable perfor- During the preparation of this work, the authors used mance across counties with diferent demographic and ChatGPT, Grammarly in order to: Grammar and spelling epidemiological characteristics. The inclusion of uncer- check, Paraphrase and reword. After using this tool/sertainty estimation allowed us to associate confidence in- vice, the authors reviewed and edited the content as tervals with each prediction, ofering health managers needed and take full responsibility for the publication’s and decision-makers an additional layer of interpretabil- content. ity and caution. This feature is especially important in a context where underestimating the future demand for References critical care resources can lead to saturation and systemic failures, while overestimating it can cause ineficient al- [1] A. Remuzzi, G. Remuzzi, Covid-19 and italy: what location. next?, The Lancet 395 (2020) 1225–1228.
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