Related Experiment Video
Updated: Nov 2, 2025

A Method of Trigonometric Modelling of Seasonal Variation Demonstrated with Multiple Sclerosis Relapse Data
Published on: December 9, 2015
Time-variant reliability-based prediction of COVID-19 spread using extended SEIVR model and Monte Carlo sampling
Mahdi Shadabfar1, Mojtaba Mahsuli1, Arash Sioofy Khoojine2,3
1Center for Infrastructure Sustainability and Resilience Research, Department of Civil Engineering, Sharif University of Technology, Tehran 145888-9694, Iran.
This study introduces a probabilistic method using an extended SEIVR model to predict COVID-19 spread in the US. The analysis forecasts decreasing active cases and increasing recoveries and fatalities by the end of 2021.
Area of Science:
- Epidemiology
- Public Health
- Biostatistics
Background:
- Coronavirus disease 2019 (COVID-19) has presented significant public health challenges globally.
- Accurate prediction of disease spread is crucial for effective intervention strategies.
- Existing models often require enhancements to incorporate factors like vaccination and quarantine.
Purpose of the Study:
- To develop and apply a probabilistic method for predicting the COVID-19 spreading profile in the United States.
- To utilize a time-variant reliability analysis framework for disease forecasting.
- To quantify the uncertainty associated with COVID-19 case predictions.
Main Methods:
- An extended susceptible-exposed-infected-vaccinated-recovered (SEIVR) deterministic model was formulated.
- The SEIVR model was integrated into a reliability framework with Monte Carlo sampling.
- Time-variant reliability analysis was employed to calculate exceedance probabilities (EPs) over time.
Main Results:
- The probabilistic model successfully predicted time-series data for infected, recovered, and deceased COVID-19 cases in the US.
- Exceedance probabilities were calculated for maximum infected, total recovered, and total fatal cases.
- 3D probability graphs illustrated the interplay between case numbers, exceedance probability, and time.
Conclusions:
- The study provides a robust probabilistic approach for forecasting epidemic dynamics.
- By the end of 2021, projections indicated approximately 0.8 million active COVID-19 cases in the US.
- The model also projected cumulative recoveries of 41.3 million and 0.6 million fatalities by the end of 2021.
Related Concept Videos
Steps in Outbreak Investigation
Prediction Intervals
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.
Statistical Methods for Analyzing Epidemiological Data
Residuals and Least-Squares Property
If the observed data point lies above the line, the residual is positive, and the line underestimates the actual data value for y. If the observed data point lies below the line, the residual is negative, and the line overestimates the actual data value for y.
The process of fitting the best-fit...
Estimating Population Standard Deviation
Causality in Epidemiology

