标题： 比较确定性与随机SIS流行病模型的行为 显示英文标题

标题： Comparing the Behaviour of Deterministic and Stochastic Model of SIS Epidemic

摘要： 自19世纪以前，就已经开展了关于流行病建模的研究。 确定性模型和随机模型都被用来捕捉人口中感染的动态。 该项目的目的是研究当设定基本再生数$R_0$时，这些模型的行为。 该数量定义为一个典型感染者在人群中对易感者的预期接触数。 根据流行病阈值理论，当$R_0 \leq 1$时，两种方法中都会以概率一发生小规模流行病，但当$R_0 > 1$时，确定性模型和随机模型的解释不同。 在确定性方法中，当$R_0 > 1$时，以概率一发生大规模流行病，并预测疾病将稳定到地方性平衡状态。 另一方面，随机模型则指出小规模流行病可能发生。 如果发生，则流行病将迅速消退。 此外，如果我们让种群规模很大且大规模流行病发生，则它会迅速爆发并达到地方性水平，并在确定性平衡点附近随机移动。 显示英文摘要

摘要： Studies about epidemic modelling have been conducted since before 19th century. Both deterministic and stochastiic model were used to capture the dynamic of infection in the population. The purpose of this project is to investigate the behaviour of the models when we set the basic reproduction number, $R_0$. This quantity is defined as the expected number of contacts made by a typical infective to susceptibles in the population. According to the epidemic threshold theory, when $R_0 \leq 1$, minor epidemic occurs with probability one in both approaches, but when $R_0 > 1$, the deterministic and stochastic models have different interpretation. In the deterministic approach, major epidemic occurs with probability one when $R_0 > 1$ and predicts that the disease will settle down to an endemic equilibrium. Stochastic models, on the other hand, identify that the minor epidemic can possibly occur. If it does, then the epidemic will die out quickly. Moreover, if we let the population size be large and the major epidemic occurs, then it will take off and then reach the endemic level and move randomly around the deterministic's equilibrium.