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Forecasting an Epidemic Diffusion Using Simulation Techniques

  • 전영아 (아주대학교 경영대학원)

초록/요약

Part Ⅰ This research forecasts the spread of COVID-19 using the Modified SEIRD (M-SEIRD) model, a class of stochastic epidemic diffusion models. The proposed model M-SEIRD model represents the disease diffusion by partitioning the population into five compartments: Susceptible, Exposed, Infected, Recovered, and Death. To estimate model parameters, the Monte Carlo Expectation–Maximization (MCEM) algorithm and the stochastic chemical reaction model are used. By conducting stochastic simulations, we derive confidence and forecasting intervals that reflect the intrinsic variability of the underlying transition processes. In addition, the minimum and maximum simulated values are presented. Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE) and Mean Absolute Deviation (MAD) are calculated to compare the performance of the M-SEIRD and SIR model. The results show that the proposed model provides a more adequate fit to the observed data. In addition, forecasting interval using simulation technique is going to guide policy makers to make a better decision to cope with epidemic diffusion. Part Ⅱ In this research, automatic change-point detection method is studied. Coefficient-of-variation (CV) and a threshold-based decision rule are used to propose a new change point detection. In M-SEIRD model, parameter estimation adopts stochastic epidemic diffusion model, combining the Monte Carlo Expectation–Maximization (MCEM) algorithm with a stochastic chemical reaction framework. By conducting stochastic simulations, confidence and forecasting intervals for the infection passways are derived. In addition, the minimum and maximum simulated values are presented. The change-point-based segment analysis identifies structural changes in the transmission process. The associated time-varying transition rates are derived based on the automatic change points. Mean Absolute Percentage Error (MAPE), Root Mean Squared Error (RMSE) and Mean Absolute Deviation (MAD) are calculated. The results show that the proposed change-point detection works well. The proposed automatic change-point detection demonstrates that structural transitions can be well identified along with manual detection. Therefore, we suggest that the automatic chang-point detection and manual detection should be incorporated. Furthermore, forecasting interval using simulation technique with automatic and manual detection is going to guide policy makers to make a better decision to cope with epidemic diffusion.

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목차

Part Ⅰ. Stochastic Epidemic Modeling and Forecasting 1
1. Introduction 2
1.1. Research Background and Objectives 2
1.2. Research Methodology and Structure 10
2. Literature Review 12
2.1. Classical Epidemic Diffusion Models 12
2.1.1. Overview of Epidemic Diffusion Models 12
2.2. Deterministic Epidemic Modeling: Types and Structural Frameworks 15
2.2.1. SI Model 15
2.2.2. SIR Model 17
2.2.3. SIRS Model 19
2.2.4. SEIR Model 21
2.3. Stochastic Epidemic Diffusion Models 23
2.3.1. Stochastic chemical reaction model 23
2.3.2. Types and Structures of Stochastic Epidemic Diffusion Models 24
2.3.2.1. Stochastic SIR Model 24
2.3.2.2. Stochastic SEIR Model 24
3. Research Methodology 26
3.1. Gillespie Algorithm 26
3.2. MLE (Maximum Likelihood Estimation) 28
3.3. EM (Expectation–Maximization) 30
3.4. MCEM (Monte Carlo Expectation–Maximization) 33
4. Research Model 38
4.1. Modified SEIRD Model 38
5. Data Analysis 43
6. Results 46
6.1. SIR Mode vs M-SEIRD Model 46
7. Conclusion 55
Part Ⅱ. Automatic Change Point Detection in M-SEIRD Model 56
1. Introduction 57
2. Literature Review 60
3. Detecting change-point 64
3.1. Coefficient of Variation 64
3.2. Implementation 71
4. M-SEIRD Model Fitting & Results 73
5. Conclusion 80
References 82
Appendix 94

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