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Register a new userA Hierarchical Bayesian Model for Stochastic Spatiotemporal SIR Modeling and Prediction of COVID-19 Cases and Hospitalizations
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Curtis Storlie
Publication date
2021
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Mathematical Statistics
and research's language is
English
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Most COVID-19 predictive modeling efforts use statistical or mathematical models to predict national- and state-level COVID-19 cases or deaths in the future. These approaches assume parameters such as reproduction time, test positivity rate, hospitalization rate, and social intervention effectiveness (masking, distancing, and mobility) are constant. However, the one certainty with the COVID-19 pandemic is that these parameters change over time, as well as vary across counties and states. In fact, the rate of spread over region, hospitalization rate, hospital length of stay and mortality rate, the proportion of the population that is susceptible, test positivity rate, and social behaviors can all change significantly over time. Thus, the quantification of uncertainty becomes critical in making meaningful and accurate forecasts of the future. Bayesian approaches are a natural way to fully represent this uncertainty in mathematical models and have become particularly popular in physics and engineering models. The explicit integration time varying parameters and uncertainty quantification into a hierarchical Bayesian forecast model differentiates the Mayo COVID-19 model from other forecasting models. By accounting for all sources of uncertainty in both parameter estimation as well as future trends with a Bayesian approach, the Mayo COVID-19 model accurately forecasts future cases and hospitalizations, as well as the degree of uncertainty. This approach has been remarkably accurate and a linchpin in Mayo Clinics response to managing the COVID-19 pandemic. The model accurately predicted timing and extent of the summer and fall surges at Mayo Clinic sites, allowing hospital leadership to manage resources effectively to provide a successful pandemic response. This model has also proven to be very useful to the state of Minnesota to help guide difficult policy decisions.
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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 (mean absolute percentage error below 15%). Moreover, we observed that, when the model is trained on a suitable two-week period around the hospitalization peak for Belgium, it forecasts the subsequent three-month decrease with mean absolute percentage error below 10%. However, when it is trained in the increase phase, it is less successful at forecasting the subsequent evolution.
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The unprecedented coronavirus disease 2019 (COVID-19) pandemic is still a worldwide threat to human life since its invasion into the daily lives of the public in the first several months of 2020. Predicting the size of confirmed cases is important for countries and communities to make proper prevention and control policies so as to effectively curb the spread of COVID-19. Different from the 2003 SARS epidemic and the worldwide 2009 H1N1 influenza pandemic, COVID-19 has unique epidemiological characteristics in its infectious and recovered compartments. This drives us to formulate a new infectious dynamic model for forecasting the COVID-19 pandemic within the human mobility network, named the SaucIR-model in the sense that the new compartmental model extends the benchmark SIR model by dividing the flow of people in the infected state into asymptomatic, pathologically infected but unconfirmed, and confirmed. Furthermore, we employ dynamic modeling of population flow in the model in order that spatial effects can be incorporated effectively. We forecast the spread of accumulated confirmed cases in some provinces of mainland China and other countries that experienced severe infection during the time period from late February to early May 2020. The novelty of incorporating the geographic spread of the pandemic leads to a surprisingly good agreement with published confirmed case reports. The numerical analysis validates the high degree of predictability of our proposed SaucIR model compared to existing resemblance. The proposed forecasting SaucIR model is implemented in Python. A web-based application is also developed by Dash (under construction).
The current outbreak is known as Coronavirus Disease or COVID-19 caused by the virus SAR-COV-2 which continues to wreak havoc across the globe. The World Health Organization (WHO) has declared the outbreak a Public Health Emergency of International Concern. In Pakistan, the spread of the virus is on the rise with the number of infected people and causalities rapidly increasing. In the absence of proper vaccination and treatment, to reduce the number of infections and casualties, the only option so far is to educate people regarding preventive measures and to enforce countrywide lock-down. Any strategy about the preventive measures needs to be based upon detailed analysis of the COVID-19 outbreak and accurate scientific predictions. In this paper, we conduct mathematical and numerical analysis to come up with reliable and accurate predictions of the outbreak in Pakistan. The time-dependent Susceptible-Infected-Recovered (SIR) model is used to fit the data and provide future predictions. The turning point of the peak of the pandemic is defined as the day when the transmission rate becomes less than the recovering rate. We have predicted that the outbreak will reach its maximum peak occurring from late May to 9 June with unrecovered number of Infectives in the range 20000-47000 and the cumulative number of infected cases in the range of 57500-153100. The number of Infectives will remain at the lower end in the lock-down scenario but can rapidly double or triple if the spread of the epidemic is not curtailed and localized. The uncertainty on single day projection in our analysis after April 15 is found to be within 5%.
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