易感性不同的病毒携带者流行病在开放系统的随机模型

A Stochastic Model for a Carrier-Borne Epidemic with Different Susceptibilities in an Opening Community

随着社会的发展 ,人口的流动越来越频繁 ,已不存在完全封闭的人群 ,以往封闭系统的流行病模型已不适合 .本文为了精确模型 ,使其更适合于流行病 ,为流行病的预测、预防及治疗提供更多、更准确的信息和措施 ,把易感者根据其由于年龄、身体状况、社会流动性等不同而引起的对流行病的易感性的明显不同分成 k类 ,在允许易感者和携带者均有移民的开放系统建立了随机模型 ,用辅助方程及递推法求得方程的解 ,并讨论了迁移率对其流行病部分指标的影响 .

With the development of the community, the mobility of population is far more frequent with no completely closing groups of people at all, and so the epidemic model for closing groups is no longer suitable now. This paper, through the extension of the model, aims to make it more suitable for the forecast, prevention, and curing of the epidemic by providing more information and methods. According to age, physical conditions, the mobility, etc, the susceptibility of varying groups is classified into S 1,S 2,…,S k. Under those conditions, a stochastic model is founded for the opening communities permitting the migrations with susceptibilities and carriers. At last, the solutions of the equations are obtained through the methods of recurrence and the supplementary equations, and the influence of the migration rates on part of indexes of the epidemic is discussed.