以傳染病數學模型探索腸病毒71型

Exploring Enterovirus 71 by Using Mathematical Models

凌書毅(Shu-yi Ling)

指導教授 ： 莊陸翰

大同大學/電機資訊學院/應用數學學系所/碩士(2008年)

摘要

為了建構出一個專用來探索在腸病毒症候群中，具有最高的併發重症率與致死率的71型的傳染病數學模型，本文參考四個傳統的傳染病數學模型，以及在SARS流行期間用來預測疫情的兩個數學模型SEIJR和SIJR，並依據腸病毒71型的機理；建構出一個非線性的微分方程組，此數學模型在本文中暫被稱為SICR。
我們藉由SICR的解來模擬腸病毒疫情的發展，再從中尋覓控制疫情的良策；經分析模型中各參數對疫情的演化影響，發現病患隔離參數在疫情控制上扮演著最重要的角色，如範例所示。文中所呈現的SICR數學模型與一些數值實驗結果，可提供一些因應措施，作為幾乎是年年流行且年年變種的腸病毒症候群的防治參考。
截至目前為止，疫情數據仍相當欠缺，所以在僅能從公開資訊中整理估算疫情參數值的情況下；SICR模型數值實驗中僅能採用精準度偏低的參數值；以致模擬的精準度亦不高。欲改善此缺點仍有賴醫療資訊方面的協助。

關鍵字

腸病毒71型 ； 腸病毒併發重症 ； 傳染病數學模型 ； SEIJR模型 ； SIJR模型 ； 隔離

並列摘要

In order to investigate enterovirus 71,which has the highest severe complications rate and the lethality in enterovirus syndrome, we tried to construct an epidemic model to explore possible preventions of the infectious disease. This paper refered to four traditional epidemic models and two epidemic models(SEIJR and SIR epidemic model) which were used to forecast the epidemic situation and construct a differential equation model according to the mechanism of enterovirus 71.This mathematical model was temporarily called SICR epidemic model in this paper.
After we simulated the development of epidemic situation with the solution of SICR epidemic model, we came up a good plan to control epidemic situation to analyze the parameter values of model that influenced epidemic situation evolved. We discovered the quarantining parameter was the most important factor to control epidemic situation, as shown in the examples. The SICR epidemic model and the result of experiment by numerical analysis may offer some preventions with reference to controlling epidemic situation of enterovirus syndrome.
Until now, we were still short of epidemic situation data, therefore we only could reorganize the estimate epidemic situation parameter value from the public information. The value of experiment in the SICR epidemic model could not only use the precise parameter value, but the precision in simulation. To improve this shortcoming, it was still necessary to depend on the assistance of the medical information.

並列關鍵字

severe complications ； epidemic model ； SEIJR epidemic model ； enterovirus 71 ； SIJR epidemic model ； quarantine

參考文獻

[4] 行政院衛生署疾病管制局官方網站：

[6] Guang Zhao Zeng, Lan Sun Chen, Li Hua Sun, Complexity of an SIR

outbreak in Ontario, Hong Kong and Singapore: the role of diagnosis

Analysis of an SIR Epidemic Model with Pulse Vaccination

Bifurcation of Solutions of an Seirepidemic Model with Vertical