隨著物聯網的概念在近代網路中的興起以及普及，越來越多的惡意軟體開始透過 物連網路進行傳播，為物聯網中的資訊安全增加了不少威脅。因此藉由在物聯網 中建立準確的數學建模來達到了解惡意軟體在物聯網中的傳播就變成了一項重要 的課題，基於對傳染病理論以及其模型的啟發，許多論文藉由分析惡意軟體的漣 漪傳播行為進而去推導出該惡意軟體的傳播建模，然而因為物聯網中裝置的移動 性以及其複雜的傳播途徑，導致所建立的數學建模並不是那麼的準確。在這篇論 文中，我們考量了物聯網惡意軟體的數量分布並提出一個新的數學建模來達到更 準確的傳播速率模型，除此之外，基於推導的建模，我們更提出了一個條件轉換 的判斷式用以確立所使用的數量分布之合法性，最後我們總結我們的建模，提出 了一個公式用來簡單的判斷該網路是否達到傳染病臨界值，最後的實驗結果也驗 證了我們的建模和真實資料相當的契合。

With the increasing use of Interent of Things (IoT) in current network, more and more malware can launch attack through IoT network, and poses a critical threat to network security. Accurate malware propagation modeling in IoT network rep- resents a fundamental research issue which show how malware dynamic infected. Inspired from epidemiology, many paper analyze the mixed behaviors of delocalized infection and ripple-based propagation for the hybrid malware in IoT network by SI model. Howerver, this kind of model will overestimate the malware infected rate. Because the node mobility is random and node infected is not always ripple-based propagation. In this paper. We consider how malware propagates in network and infected node size distrubution. We formula a modify propage model based on SI model to analyze infection rate to t real network trace accuratly. Since we consider di erent size distrubution in di erent time stage, we need to give a transition condi- tion to make distrubution conform the network propagation rate. Our contribution is presente a stage transition condition to determine suitable size distrubution to formula model. Otherwise, based on our formulation, we give a judgment to quickly determine if the network will be completely paralyzed. Finaly, we compare other proposed model in real dataset and the result shows that experiments have been more closer to real data.

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