在這篇論文中，我們提出一個兩層次混合隨機傳染病模型，其中的傳佈參數是可以隨時間改變的。 我們以家中至少有一人感染的家庭為基本單位，同時考慮家中的感染率及全區的感染率。因為不同的家庭 開始感染的時間常常不同，而且傳染病控制的措施也隨著時間作改變。所以，讓模型中感染率及隔離率隨時間改變 是一個合理的期望。由於感染時間不易取得，我們只以每家感染者的隔離時間為資料作估計。我們用這個模型估計 一個常被引用的天花傳染病的資料，與之前一些學者的估計作比較，結果顯示我們的模型也可以得出近似的值，但更 精緻些，可以有更多推論。此外，我們也作了一個模擬的研究。 This paper proposes a two-level mixing stochastic epidemic model in which the transmission parameters may change over time. We take households that have at least one infective as the standard unit in the study and consider both a within-household infection rate and a global infection rate. In view of the fact that outbreaks may happen at different time points in different households and control measures may change over time, it is desirable to allow these infection rates and the removal rates varying with time. We study in this paper the temporal infection rates and removal rates based on only the removal times in each household, since the infection times are usually not observable. We apply our model to the classic smallpox epidemic dataset occuring in a closed community of 120 individuals in Abakaliki, Nigeria. The estimation results seem to suggest that our more sophisticated method at least works. A simulation study is also carried out.
