COVID-19 pandemic has had a disruptive and irreversible impact globally, yet traditional epidemiological modeling approaches such as the susceptible-infected-recovered (SIR) model have exhibited limited effectiveness in forecasting of the up-to-date pandemic situation. In this work, susceptible-vaccinated-exposed-infected-dead-recovered (SVEIDR) model and its variants -- aged and vaccination-structured SVEIDR models -- are introduced to encode the effect of social contact for different age groups and vaccination status. Then, we implement the physics-informed neural network (PiNN) on both simulated and real-world data. The PiNN model enables robust analysis of the dynamic spread, prediction, and parameter optimization of the COVID-19 compartmental models. The models exhibit relative root mean square error (RRMSE) of $<4\%$ for all components and provide incubation, death, and recovery rates of $γ= 0.0130$, $λ=0.0001$, and $ρ=0.0037$, respectively, for the first 310 days of the epidemic in the US with RRMSE of $<0.35\%$ for all components. To further improve the model performance, temporally varying parameters can be included, such as vaccination, transmission, and incubation rates. Our implementation highlights PiNN as a reliable candidate approach for forecasting real-world data and can be applied to other compartmental model variants of interest.
Approaching epidemiological dynamics of COVID-19 with physics-informed neural networks
Frankfurt Institute for Advanced Studies（法兰克福高等研究院）；Xidian-FIAS International Joint Research Center（西安电子科技大学-法兰克福高等研究院国际联合研究中心）；Institut für Theoretische Physik, Goethe Universität Frankfurt（法兰克福大学理论物理研究所）；GSI Helmholtzzentrum für Schwerionenforschung GmbH（GSI亥姆霍兹重离子研究中心）；Xidian University（西安电子科技大学）
本文提出将嵌入 SIR 模型的物理信息神经网络（PINN）用于传染病动力学建模，通过在合成数据和德国 COVID-19 数据上的实验证明其能准确识别和预测疫情传播趋势，展示了机器学习与仓室模型结合研究流行病的高潜力。
We propose a novel approach that integrates machine learning into compartmental disease modeling to predict the progression of COVID-19. Our model is explainable by design as it explicitly shows how different compartments evolve and it uses interpretable encoders to incorporate covariates and improve performance. Explainability is valuable to ensure that the model's forecasts are credible to epidemiologists and to instill confidence in end-users such as policy makers and healthcare institutions. Our model can be applied at different geographic resolutions, and here we demonstrate it for states…
This is work in progress. We make it accessible hoping that people might find the idea useful. We propose a discrete, recursive 5-compartment model for the spread of epidemics, which we call {\em SEPIR-model}. Under mild assumptions which typically are fulfilled for the Covid-19 pandemic it can be used to reproduce the development of an epidemic from a small number of parameters closely related to the data. We demonstrate this at the development in Germany and Switzerland. It also allows model predictions assuming nearly constant reproduction numbers. Thus it might be a useful tool for sheddin…
We propose the SH model, a simplified version of the well-known SIR compartmental model of infectious diseases. With optimized parameters and initial conditions, this time-invariant two-parameter two-dimensional model is able to fit COVID-19 hospitalization data over several months with high accuracy (e.g., the root relative squared error is below 10% for Belgium over the period from 2020-03-15 to 2020-07-15). Moreover, we observed that, when the model is trained on a suitable three-week period around the first hospitalization peak for Belgium, it forecasts the subsequent two months with mean …
Integrating Spatiotemporal Features in LSTM for Spatially Informed COVID-19 Hospitalization Forecasting
Heilbrunn Department of Population and Family Health, Columbia University Mailman School of Public Health（哥伦比亚大学流行病学与家庭健康系）；Department of Geography, University of Colorado（科罗拉多大学地理系）；Population Council（人口理事会）
The recent coronavirus disease (COVID-19) outbreak has dramatically increased the public awareness and appreciation of the utility of dynamic models. At the same time, the dissemination of contradictory model predictions has highlighted their limitations. If some parameters and/or state variables of a model cannot be determined from output measurements, its ability to yield correct insights -- as well as the possibility of controlling the system -- may be compromised. Epidemic dynamics are commonly analysed using compartmental models, and many variations of such models have been used for analy…
With COVID-19 affecting every country globally and changing everyday life, the ability to forecast the spread of the disease is more important than any previous epidemic. The conventional methods of disease-spread modeling, compartmental models, are based on the assumption of spatiotemporal homogeneity of the spread of the virus, which may cause forecasting to underperform, especially at high spatial resolutions. In this paper we approach the forecasting task with an alternative technique - spatiotemporal machine learning. We present COVID-LSTM, a data-driven model based on a Long Short-term M…
Compartment models of cell culture are widely used in cytology, pharmacology, toxicology and other fields. Numerical simulation, data modeling and prediction of compartment models can be realized by traditional differential equation modeling methods. At the same time, with the development of software and hardware, Physical Informed Neural Network (PINN) is widely used to solve differential equation models. This work models, simulates and predicts the cell culture compartment model based on the machine learning framework PyTorch with an 16 hidden layers neural network, including 8 linear layers…
We present a compartmental SEIRD model aimed at forecasting hospital occupancy in metropolitan areas during the current COVID-19 outbreak. The model features asymptomatic and symptomatic infections with detailed hospital dynamics. We model explicitly branching probabilities and non exponential residence times in each latent and infected compartments. Using both hospital admittance confirmed cases and deaths we infer the contact rate and the initial conditions of the dynamical system, considering break points to model lockdown interventions. Our Bayesian approach allows us to produce timely pro…
In this paper, we estimate epidemiological data of the COVID-19 pandemic in Hungary using only the daily number of hospitalized patients, and applying well-known techniques from systems and control theory. We use a previously published and validated compartmental model for the description of epidemic spread. Exploiting the fact that an important subsystem of the model is linear, first we compute the number of latent infected persons in time. Then an estimate can be given for the number of people in other compartments. From these data, it is possible to track the time dependent reproduction num…
It is widely accepted that the number of reported cases during the first stages of the COVID-19 pandemic severely underestimates the number of actual cases. We leverage delay embedding theorems of Whitney and Takens and use Gaussian Process regression to estimate the number of cases during the first 2020 wave based on the second wave of the epidemic in several European countries, South Korea, and Brazil. We assume that the second wave was more accurately monitored and hence that it can be trusted. We then construct a manifold diffeomorphic to that of the implied original dynamical system, usin…
