CAJ | 학술논문

以动态随机图论为工具，使用分支过程近似方法，研究大人口规模下离散时间传染病模型的渐近性。结果表明：对传统的SIR 模型进行改进后，单独个体不再以相同概率与其他个体发生接触，而是以特定分布拥有一定数量的亲友；当初始患者数量不大时，用分支过程近似传染病传播过程有效；结合分支过程理论经典结果，当人群规模不断扩张时，新增患者数量将呈现几乎必然收敛性。
이동태수궤도론위공구，사용분지과정근사방법，연구대인구규모하리산시간전염병모형적점근성。결과표명：대전통적SIR 모형진행개진후，단독개체불재이상동개솔여기타개체발생접촉，이시이특정분포옹유일정수량적친우；당초시환자수량불대시，용분지과정근사전염병전파과정유효；결합분지과정이론경전결과，당인군규모불단확장시，신증환자수량장정현궤호필연수렴성。
We used the theory of dynamic random graph as the tool to investigate the convergence of a stochastic discrete-time epidemic model in a large population by means of the method of branching process approximation.The significance of the paper lies in the improved SIR model.Each individual has a certain number of acquaintances with a fixed distribution.As the number of initially infective individuals stays small,a branching process approximation for the number of infective individuals is in force.Using the results of the branching process,we will have the main results,that is,the number of new infective individuals will present some almost surely limit properties with the size of the population extending.