結核病是危害人類健康歷史久遠的慢性傳染病，是一種目前仍普遍存在於全世界，尤其是未開發及開發中國家的慢性傳染病，若給予適當的抗結核藥物治療，結核病幾乎可以百分之百痊癒（Cure）；但若不予治療，則在3年內，約有一半的病人會死亡。而目前結核病發展成致命性「抗藥性結核病」及結核病與愛滋病雙重流行，更恐將成為人類浩劫。傳染病的危害防制，是考驗著國家衛生制度的重要指標，如何能夠在有效的資源下達到預防傳染病的最佳化，是我們所關心的議題。
根據世界衛生組織的報告指出，都治計畫（DOTS）是一個最有效益的防治方法，本研究首先在傳染病模型中增加結核病患者中常見的多重抗藥性患者(Drug resistance)，並且將其影響一併加入模型中，同時並考慮一些有效防制的方法，像是推動「落實結核病人直接觀察治療（都治DOTS）計畫」、「降低傳染性結核病病人的傳播率」等方法，驗證都治計畫是否為一最有效益之方式；其次，考量多個受到結核病威脅的區域，針對該區域結核病肆虐的情形，找出預防及控制結核病最有效的資源分配方式。最後，我們以一個例子說明利用近似式找尋最佳化的進行步驟。

Tuberculosis is a chronic infectious disease which endangers the human health for a long time. It is a common disease existing in the whole world at present time, especially in the undeveloped and developing country. If properly cared, the tuberculosis patient can almost be cured. Otherwise, if not taking effective cure method, half of the tuberculosis patient will die in three years. And now the tuberculosis is developed into the mortal case – the drug resistance TB and the prevailing of the TB and AIDS which is a great calamity. The danger of the infectious disease in one country is the important index of testing system of national hygiene. How can we minimize the number of the infectious patients under the limited budget is what we are concerned.
In this thesis, first we add the common case - infection of drug resistance compartment in our epidemic model, and we also consider the transmission rate of transferring from chronic patients to drug resistance case. We provide some preventing method usually used to control tuberculosis, like DOTS and reducing the contact rate…, and so on. Second, we consider different TB situations in different regions. In any one of the regions , when we collect the data and know the distribution of TB patients in each compartment, we can find out the best resource allocation method to control the disease, Finally, we present one example to illustrate the steps how we get the optimal solution by approximating method.

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