至目前為止，傳染性疾病監測系統多以所通報之確診病例或感染發生率評 估疫情，然而在面對無症狀與輕症感染居多的疾病時，由於許多患者未被計入 確診病例，容易因未計算到疾病的潛在傳播，而低估了疫情真正的嚴重性。
對於長期盛行的傳染性疾病而言，不同年齡層的人群因所經歷的年代不 同，加上疾病感染力隨時間的變化，而有不同的感染比例。另一方面，不同的 感染比例，亦代表不同年齡層人群因過去感染疾病，而對其具免疫力的比例有 所差異。本研究透過年齡分層資料建立統計模型，分別使用貝葉斯方法與最佳 化演算法進行估計，來量化疾病的感染力以推估疫情實際的盛行情況。
本研究將此方法應用在臺灣登革熱上，在第一部分使用年齡分層感染發生 率資料，計算登革熱在大流行時期與其他時期的平均感染力，並推估登革熱在 人群的盛行率及感染通報率。本研究的結果與國內多個血清學的研究結果一 致，且更進一步提供了探討不同地區疫情長期變化的方法。第二部分則著重於 規劃大規模的登革熱血清學研究，以電腦模擬的方式探討在可取得資料的年齡 分佈下，不同樣本數對估計疾病感染力的能力；並藉由聚集性的人潮流動資 料，探討考慮地區間的人潮流動對準確評估疫情的重要性。這部分研究除了能 更有效率的分配不同地區所需採樣數，並能校正在一般血清學研究忽略的人潮 流動。綜上所述，本研究將年齡分層的分析方法應用在感染發生率或是血清學 資料上，對評估疫情長期變化提供較穩健的結果，且說明了人潮流動對評估各 區疫情的重要性。

Currently, infectious disease surveillance systems usually assess the risk of infectious diseases based on the number of confirmed cases or incidence rate. However, for infectious diseases with many asymptomatically or mildly symptomatic infections, the transmission intensity of infectious diseases is likely underestimated and the potential transmission chains are likely missed because these infections are usually not captured by the surveillance system.
For infectious diseases that have been prevalent for a long period of time, the infection rates differ between age groups because they experience different years of transmission, and the transmission intensity changes through time. On the other hand, the different infection rates in different age groups also represent the difference in their proportions of people who are immune to the disease due to past infections. In this study, age-specific statistical models were developed to quantify the transmission intensity of infectious diseases and estimate the actual prevalence, and the parameters in the models were estimated using either Bayesian method or optimization algorithms.
We applied this method to dengue data in Taiwan. In the first part, we used age stratified incidence data to estimate the force of infection (FOI) of dengue during bigger outbreak years and other periods, followed by estimating the prevalence and reporting rate of dengue. The results are consistent with other serological studies in Taiwan, and further provide an approach to examine the long-term transmission intensity in different cities. The second part of the thesis focuses on designing a large scale serological study of dengue. I used computer simulations to investigate the impact of sample size on the ability to estimate the force of infection of the disease given the age distribution of the available data, as well as make use of the aggregated human mobility data in Taiwan to assess the importance of considering intercity movements on the estimation of transmission intensity. This part of the study not only provides insights into the allocation of sample size across regions, but also corrects for human mobility, which has been neglected in other studies. Overall, this study applied age-stratified methods to incidence and serological data, providing more robust estimates of long-term changes in the transmission intensity and demonstrating the importance of incorporating human movements when estimating transmission intensity in multiple regions.

摘要 ii
Abstract iii
誌謝 iv
目錄 v
圖目錄 viii
表目錄 ix
第一章 緒論 1
第二章 材料方法 6
2-1 相關名詞解釋 6
2-1-1感染發生率 (incidence rate): 6
2-1-2疾病大流行 (outbreak)與地方性傳染病 (endemic): 6
2-1-3有效傳染數 (effective reproduction number) 7
2-1-4平均感染力 (force of infection, FOI): 7
2-1-5感染通報率 (reporting rate): 7
2-1-6 最大似然估計 (Maximum likelihood estimate, MLE): 8
2-1-7馬可夫鏈蒙地卡羅方法 (Markov chain Monte Carlo, MCMC): 8
2-2 研究資料 9
2-2-1登革熱確診病例資料： 9
2-2-2人口資料： 9
2-2-3血清來源資料庫： 10
2-2-4人潮流動資料： 10
第三章 統計模型 11
3-1 年齡分層感染發生率模型 11
3 -1-1 數學符號說明 11
3-1-2 建立統計模型 13
3-1-3 以馬可夫鏈蒙地卡羅方法進行參數估計 15
3-1-4 推估實際感染登革熱人數 15
3-1-5 計算血清陽性率 16
3-2年齡分層血清模型 16
3-2-1 數學符號說明 17
3-2-2 建立統計模型與最大似然估計 18
第四章 研究結果 20
4-1 以年齡分層感染發生率資料估計登革熱的傳播情形 20
4-1-1模型設立與資料校正 20
4-1-2參數估計及電腦模擬分析 22
4-1-3 估計登革熱平均感染力與實際感染人數 29
4-1-4登革熱盛行率估計 32
4-1-5登革熱感染通報率估計 34
4-2 以模擬的方式幫助規劃目標為估計感染力的血清學研究 35
4-2-1 探討樣本資料可估計的平均感染力範圍 35
4-2-2探討估計平均感染力隨時間變化的能力 37
4-2-3 人群移動對估計登革熱平均感染力的影響 39
第五章 討論 42
第六章 參考資料 45
第七章 附錄 49

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