Title Page
Contents
ABSTRACT 11
Ⅰ. Introduction 13
1.1. Motivation 13
1.2. Ebolavirus Disease Outbreaks and Challenges 16
1.3. Transmission Dynamics of Middle Eastern Respiratory Syndrome and the Role of Hospitals and Cultural Practices in Korea 18
1.4. Mathematical and Statistical Modeling in Infectious Disease Dynamics 21
Ⅱ. Materials and Methods 24
2.1. Dynamics of the SIR Model 25
2.2. Stochastic Modeling of Infectious Diseases: The Gillespie Algorithm and 28
2.3. Parameter Estimation : Maximum Likelihood Estimation and Metropolis-Hastings Approach 34
Ⅲ. Analysis of the Ebolavirus Disease Outbreak Incorporating Unreported Cases and the Delays s in Detection 41
3.1. Modeling Ebolavirus Disease Outbreak Incorporating Medical Staffs and Reporting Variabilities 42
3.2. Simulation Results Based on 2022 Uganda Outbreak and Impact of Nonpharmaceutical Interventions 47
3.3. Impact of Outbreak Declaration Timing and Intensity of Nonpharmaceutical Interventions 60
3.4. Summary of the Ebolavirus Disease Outbreak Simulation 66
Ⅳ. Modeling the Outbreak of Middle East Respiratory Syndrome with Consideration of Intra- and Inter-Hospital Transmission 68
4.1. Intra-hospital Transmission Model 69
4.1.1. Analysis of Pyeongtaek St. Mary's Hospital Case 69
4.1.2. Impact of Hospital Stay Duration of Index Case 82
4.1.3. Summary of the Intra-hospital Outbreak Simulation 84
4.2. A Stratified Model for Transmission within Single Hospital 85
4.2.1. A Model Considering Superspreading Event at Samsung Medical Center 85
4.2.2. Scenario-based Study Considering Adjustable Risk 94
4.2.3. Summary of the Simulation Considering a a Superspreader 100
4.3. Inter-hospital Transmission Model 102
4.3.1. Model Formulation and Regional Characteristics 102
4.3.2. Baseline Model Simulation Results 109
4.3.3. Community Spread Risk Due to Detection Delay 122
4.3.4. Preventive Effect of Mask Mandates 131
4.3.5. Scenarios Considering Higher Local Transmissibility 135
4.3.6. Potential Risk of Superspreading Event 140
4.3.7. Summary of the Inter-hospital Outbreak Simulation 153
Ⅴ. Discussions 155
5.1. Ebolavirus Disease Outbreak Simulation 156
5.2. Middle East Respiratory Syndrome Outbreak Simulation 159
5.2.1. Intra-hospital Outbreak 159
5.2.2. Inter hospital Outbreak 163
Ⅵ. Conclusion 168
6.1. Risk Assessment of Ebolavirus Disease Outbreak 168
6.2. Multifaceted Approach of Middle East Respiratory Syndrome Outbreak 169
6.3. Limitations and Future Work Suggestion 171
References 172
ABSTRACT (in Korean) 184
Table 3.1. Characteristics of the propensity of nondelayed events and intricacies of delayed events. 46
Table 4.1. Description of nondelayed and delayed reactions in MERS intra-hospital transmission model 78
Table 4.2. Propensity of nondelayed reactions in intra-hospital MERS outbreak model considering two groups. 91
Table 4.3. Summarized results of Figure 4.28. The value inside the parentheses below average indicates the increase compared to the... 137
Figure 2.1. Flow diagram of SIR model. Each arrow indicates the transition of the status of hosts. 25
Figure 2.2. Two possible cases in modified Gillespie algorithm: The case when t +τ 〈τ* (A), the case when t + τ〉 τ* (B). Here, t represents... 33
Figure 2.3. Epidemiological process of hypothetical outbreak: Time of infection and recovery for individual hosts (A), timeline for individual... 37
Figure 2.4. Illustration of Simple MLE and MH example outcomes: Depiction of likelihood as a function of β (A), the distribution sampled... 40
Figure 3.1. Flow diagram depicting the spread of EVD, taking into account medical staffs and cases that were not reported. Solid-line... 43
Figure 3.2. Division of phases considering outbreak declaration and setting for baseline model simulation scenario. 48
Figure 3.3. Cumulative confirmed cases from the baseline model simulation: The grey curves represent individual simulation runs, the... 50
Figure 3.4. Impact of coupled NPIs post-outbreak declaration on the simulation results for confirmed cases. The dashed cyan curve represents... 52
Figure 3.5. Prevalence number over time from the baseline model simulation: Exposed individuals (A), infectious individuals (B), and... 54
Figure 3.6. Histogram representing the durations of phases: Duration from the occurrence of the primary case to the outbreak declaration (A),... 56
Figure 3.7. Visual representation via scatter plots demonstrating the correlation between the outbreak duration and its scale. The Y-Axis... 58
Figure 3.8. Distribution of prevalence by each status at the time of outbreak declaration. 59
Figure 3.9. Simulation results varying the periods leading to outbreak declaration: Simulation mean and 95% CrI of the number of confirmed... 62
Figure 3.10. Simulation results varying intensity of NPIs: Simulation mean and 95% CrI of the number of confirmed cases (A), probability of... 63
Figure 3.11. Outbreak scale determined by the intensity of NPIs and the timing of recognition. Dashed lines represent contours: yellow denotes... 65
Figure 4.1. Flow diagram of the intra-hospital MERS transmission model 70
Figure 4.2. Distribution of the disease progress transition time: Incubation period (A), duration from symptom onset to disease... 72
Figure 4.3. Epidemiological investigation of the MERS outbreak at Pyeongtaek St. Mary's Hospital (compiled from the appendix of the study... 75
Figure 4.4. Results of the MH algorithm sampling, excluding the burn-in phase: Sampling traces with a log-scaled Y-Axis (A), histograms of... 76
Figure 4.5. Baseline scenario model simulation results: Cumulative confirmed cases over time (A), distribution of the number of confirmed... 80
Figure 4.6. Distribution of outbreak duration and size: Histogram graph (A), scatter plot illustrating the correlation between the outbreak... 81
Figure 4.7. Simulation results considering different length of hospital stay of the index case: Number of cases (A), outbreak duration (B). 83
Figure 4.8. Flow diagram of intra-hospital MERS outbreak model considering different groups. 86
Figure 4.9. Implementation of the MH Algorithm for MLE in the context of the MERS outbreak at Samsung Medical Center instigated by Case #14:... 88
Figure 4.10. Baseline scenario simulation results of the single hospital outbreak model considering different groups and superspreader:... 93
Figure 4.11. Simulation results considering different infectious period of Case #14: Number of confirmed cases (A), outbreak duration (B). 95
Figure 4.12. Trend in the number of confirmed cases by varying the value of adjusting factor. Dark curve indicates the mean value from the... 97
Figure 4.13. Trend in the number of confirmed cases by varying inter-group transmission rate adjustment parameter between 0 and 1. The red... 99
Figure 4.14. Model flow diagram of MERS outbreak considering local area and intra- and inter- hospital transmission. Solid arrow lines indicate... 105
Figure 4.15. Flowchart for the simulation of MERS outbreak model. 108
Figure 4.16. Box and whisker plots of simulation results based on the hospital of entry for the index case: the number of confirmed cases (A),... 110
Figure 4.17. Information on Hospitals Located in Gangnam: Number of MS and the number of inpatients (A), ratio of inpatients to MS (B). 112
Figure 4.18. Outbreak outcomes from the simulation runs: distribution of confirmed cases (A), distribution of the number of hospitals exposed... 114
Figure 4.19. Prevalence considering the status of hosts: individuals in the exposed state (A), individuals in the infectious state (B),... 116
Figure 4.20. Prevalence at the outbreak detection considering the status of different host: incubation (exposed) stage (A), infectious stage (B). 118
Figure 4.21. Box and whisker plots of simulation categorizing the simulation results based on presence or absence of prevalence in the... 121
Figure 4.22. Impact of varying infection detection timing post-admission of the index case from 0 to 18 days on outbreak metrics. The black... 123
Figure 4.23. Depiction of prevalence at detection point. Panels A-C represent exposed, and panels D-F represent infectious MS, patients,... 125
Figure 4.24. Distribution of outbreak outcomes under varied time from the index case hospitalization to isolation scenario: Number of... 128
Figure 4.25. Impact of varying isolation duration for the index case on the number of infected individuals at outbreak recognition: The number... 130
Figure 4.26. Outbreak outcomes from model simulation considering mask mandates and the effectiveness of control using box-and-whisker plot:... 133
Figure 4.27. Prevalence number at the timing of outbreak detection considering mask mandates and the effectiveness of control using box-... 134
Figure 4.28. Simulation results considering higher transmissibility in local: Number of cases (A), number of hospitals exposed to the disease... 136
Figure 4.29. Probability that the outbreak outcome exceeds certain value: The number of confirmed cases (A), peak size of hospitalized patients... 139
Figure 4.30. Application of MH algorithm into MLE considering MERS outbreak in Samsung Medical Center caused by superspreader Case #14,... 141
Figure 4.31. Box and whisker plots of simulation results based on the hospital of entry for the superspreader: the number of cases (A), the... 144
Figure 4.32. Distribution of outbreak size considering superspreading event in different hospitals. Red dashed vertical line indicates the... 146
Figure 4.33. Mean prevalence number over time considering superspreading event in hospital #18 and #31: Prevalence in the index hospital and out... 149
Figure 4.34. Outbreak outcomes from model simulation considering superspreading events, mask mandates, and the effectiveness of control... 152