在本篇論文中，我們討論真消息和假消息同時存在網路中與個體互動的情形。我們的模型是以傳染病中經典的SIR (Susceptible-Infectious-Recovered) 模型為基礎來延伸；而我們一樣也是將個體分為三種狀態，分別代表他們是否曾經接受過消息。另外我們為了讓模型更貼近現實世界的情況，特別將能夠反映個體偏好真消息或是假消息的屬性加到模型中。接著我們利用微分方程式探討真消息和假消息在模型中傳播的情況，並且透過穩定性分析推導出最終的穩定條件。最後我們用數值結果來說明每一個狀態在模型中如何隨時間變化，而數值的結果顯示即使最初偏好真消息與假消息的個體是一樣多，不過隨著消息在模型中的傳播最終接受真消息的個體會比接受假消息的個體還要多。

In this paper, we explore the interaction between truth, misinformation, and individuals in a network where both are present simultaneously. Our model is based on the classic Susceptible-Infectious-Recovered model in infectious diseases. We also categorized individuals into three states, representing whether they have ever accepted information. Specially, we incorporate attributes that reflect individual preferences for truth or misinformation into the model. Hence, our model becomes more closely aligned with real-world situations. Besides, we utilize differential equations to investigate the dynamics of truth and misinformation propagation in our model and also analyze stability to derive the eventual stability conditions of our model. Finally, we use numerical results to illustrate how each state in our model changes over time. The numerical results demonstrate, in our model, even with an equal number of individuals having preferences for truth or misinformation at the beginning, a higher proportion of individuals participate in propagating truth rather than misinformation.

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