Since diffusion models of social network are widely used in studying epidemiology, in this thesis, we apply diffusion models to study the contact immunity generated by attenuated vaccines.Oral polio vaccine (OPV) is a typical attenuated vaccine for polio that can produce contact immunity and therefore help protect more individuals than vaccinees. / To better capture the utilization of OPV’s contact immunity, we model the community as a social network, and formulate the task of maximizing the contact immunity effect as an optimization problem on graphs, which is to find a sequence of vertices to be “vaccinated” to maximize the total number of vertices “infected” by the attenuated virus. Furthermore, as immune defiicient patients may suffer from the live attenuated virus in the vaccine, we develop models in consideration of this restriction, and study related problems. / We present polynomial-time algorithms for these problems on trees, and show the intractability of problems on general graphs. / 社交網絡的擴散模型被廣泛運用于對流行病學的研究，在本文中，我們使用擴散模型對減毒活疫苗產生的接觸性免疫進行研究。口服脊髓灰質炎疫苗（OPV）是一種典型的減毒活疫苗，它可以在人群中產生接觸性免疫，使得更多未接種疫苗的人獲得免疫力。 / 爲了更好的刻畫OPV 產生的接觸性免疫，我們將社區模型化為社交網絡，從而將接觸性免疫效應最大化的任務轉化爲圖優化問題，即通過發現頂點的一個「接種」序列來最大化被減活病毒「感染」的頂點數量。此外，因爲減毒疫苗中的活病毒會使患有免疫缺陷的病人患病，我們考慮在此因素限制下的模型，并研究相關的問題。 / 我們給出這些問題在樹上的多項式時間算法，并證明其在一般圖上的複雜性。 / Ma, Chenglong. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 40-47). / Abstracts also in Chinese. / Title from PDF title page (viewed on 12, September, 2016). / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only.