Explainability is valuable to ensure that the model's forecasts are credible

Accurate forecasting of contagious illnesses has become increasingly important to public health policymaking, and better prediction could prevent the loss of millions of lives. To better prepare for future pandemics, it is essential to improve forecasting methods and capabilities. In this work, we propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging area of scientific machine learning. The proposed PINN model incorporates dynamical systems representations of disease transmission into the loss function, thereby assimilating epidemiological theory and data using neural networks (NNs). Our approach is designed to prevent model overfitting, which often occurs when training deep learning models with observation data alone. In addition, we employ an additional sub-network to account for mobility, vaccination, and other covariates that influence the transmission rate, a key parameter in the compartment model. To demonstrate the capability of the proposed model, we examine the performance of the model using state-level COVID-19 data in California. Our simulation results show that predictions of PINN model on the number of cases, deaths, and hospitalizations are consistent with existing benchmarks. In particular, the PINN model outperforms the basic NN model and naive baseline forecast. We also show that the performance of the PINN model is comparable to a sophisticated Gaussian infection state space with time dependence (GISST) forecasting model that integrates the compartment model with a data observation model and a regression model for inferring parameters in the compartment model. Nonetheless, the PINN model offers a simpler structure and is easier to implement. Our results show that the proposed forecaster could potentially serve as a new computational tool to enhance the current capacity of infectious disease forecasting.

Malaria is one of the deadliest diseases in the world, every year millions of people become victims of this disease and many even lose their lives. Medical professionals and the government could take accurate measures to protect the people only when the disease dynamics are understood clearly. In this work, we propose a compartmental model to study the dynamics of malaria. We consider the transmission rate dependent on temperature and altitude. We performed the steady state analysis on the proposed model and checked the stability of the disease-free and endemic steady state. An artificial neural network (ANN) is applied to the formulated model to predict the trajectory of all five compartments following the mathematical analysis. Three different neural network architectures namely Artificial neural network (ANN), convolution neural network (CNN), and Recurrent neural network (RNN) are used to estimate these parameters from the trajectory of the data. To understand the severity of a disease, it is essential to calculate the risk associated with the disease. In this work, the risk is calculated using dynamic mode decomposition(DMD) from the trajectory of the infected people.

Classical compartmental models in epidemiology often struggle to accurately capture real-world dynamics due to their inability to address the inherent heterogeneity of populations. In this paper, we introduce a novel approach that incorporates heterogeneity through a mobility variable, transforming the traditional ODE system into a system of integro-differential equations that describe the dynamics of population densities across different compartments. Our results show that, for the same basic reproduction number, our mobility-based model predicts a smaller final pandemic size compared to classic compartmental models, whose population densities are represented as Dirac delta functions in our density-based framework. This addresses the overestimation issue common in many classical models. Additionally, we demonstrate that the time series of the infected population is sufficient to uniquely identify the mobility distribution. We reconstruct this distribution using a machine-learning-based framework, providing both theoretical and algorithmic support to effectively constrain the mobility-based model with real-world data.

Dynamic Positron Emission Tomography (dPET) imaging and Time-Activity Curve (TAC) analyses are essential for understanding and quantifying the biodistribution of radiopharmaceuticals over time and space. Traditional compartmental modeling, while foundational, commonly struggles to fully capture the complexities of biological systems, including non-linear dynamics and variability. This study introduces an innovative data-driven neural network-based framework, inspired by Reaction Diffusion systems, designed to address these limitations. Our approach, which adaptively fits TACs from dPET, enables the direct calibration of diffusion coefficients and reaction terms from observed data, offering significant improvements in predictive accuracy and robustness over traditional methods, especially in complex biological scenarios.

Since infectious pathogens start spreading into a susceptible population, mathematical models can provide policy makers with reliable forecasts and scenario analyses, which can be concretely implemented or solely consulted. In these complex epidemiological scenarios, machine learning architectures can play an important role, since they directly reconstruct data-driven models circumventing the specific modelling choices and the parameter calibration, typical of classical compartmental models. In this work, we discuss the efficacy of Kernel Operator Learning (KOL) to reconstruct population dynamics during epidemic outbreaks, where the transmission rate is ruled by an input strategy. In particular, we introduce two surrogate models, named KOL-m and KOL-$\partial$, which reconstruct in two different ways the evolution of the epidemics. Moreover, we evaluate the generalization performances of the two approaches with different kernels, including the Neural Tangent Kernels, and compare them with a classical neural network model learning method. Employing synthetic but semi-realistic data, we show how the two introduced approaches are suitable for realizing fast and robust forecasts and scenario analyses, and how these approaches are competitive for determining optimal intervention strategies with respect to specific performance measures.

Epidemiological models are best suitable to model an epidemic if the spread pattern is stationary. To deal with non-stationary patterns and multiple waves of an epidemic, we develop a hybrid model encompassing epidemic modeling, particle swarm optimization, and deep learning. The model mainly caters to three objectives for better prediction: 1. Periodic estimation of the model parameters. 2. Incorporating impact of all the aspects using data fitting and parameter optimization 3. Deep learning based prediction of the model parameters. In our model, we use a system of ordinary differential equations (ODEs) for Susceptible-Infected-Recovered-Dead (SIRD) epidemic modeling, Particle Swarm Optimization (PSO) for model parameter optimization, and stacked-LSTM for forecasting the model parameters. Initial or one time estimation of model parameters is not able to model multiple waves of an epidemic. So, we estimate the model parameters periodically (weekly). We use PSO to identify the optimum values of the model parameters. We next train the stacked-LSTM on the optimized parameters, and perform forecasting of the model parameters for upcoming four weeks. Further, we fed the LSTM forecasted parameters into the SIRD model to forecast the number of COVID-19 cases. We evaluate the model for highly affected three countries namely; the USA, India, and the UK. The proposed hybrid model is able to deal with multiple waves, and has outperformed existing methods on all the three datasets.

Epidemiological compartmental models are useful for understanding infectious disease propagation and directing public health policy decisions. Calibration of these models is an important step in offering accurate forecasts of disease dynamics and the effectiveness of interventions. In this study, we present an overview of calibrating strategies that can be employed, including several optimization methods and reinforcement learning (RL). We discuss the benefits and drawbacks of these methods and highlight relevant practical conclusions from our experiments. Optimization methods iteratively adjust the parameters of the model until the model output matches the available data, whereas RL uses trial and error to learn the optimal set of parameters by maximizing a reward signal. Finally, we discuss how the calibration of parameters of epidemiological compartmental models is an emerging field that has the potential to improve the accuracy of disease modeling and public health decision-making. Further research is needed to validate the effectiveness and scalability of these approaches in different epidemiological contexts. All codes and resources are available on https://github.com/Nikunj-Gupta/

Infectious diseases, either emerging or long-lasting, place numerous people at risk and bring heavy public health burdens worldwide. In the process against infectious diseases, predicting the epidemic risk by modeling the disease transmission plays an essential role in assisting with preventing and controlling disease transmission in a more effective way. In this paper, we systematically describe how machine learning can play an essential role in quantitatively characterizing disease transmission patterns and accurately predicting infectious disease risks. First, we introduce the background and motivation of using machine learning for infectious disease risk prediction. Next, we describe the development and components of various machine learning models for infectious disease risk prediction. Specifically, existing models fall into three categories: Statistical prediction, data-driven machine learning, and epidemiology-inspired machine learning. Subsequently, we discuss challenges encountered when dealing with model inputs, designing task-oriented objectives, and conducting performance evaluation. Finally, we conclude with a discussion of open questions and future directions.