van Herwaarden O A, Grasman J
Department of Mathematics, Agricultural University, Wageningen, The Netherlands.
J Math Biol. 1995;33(6):581-601. doi: 10.1007/BF00298644.
A study is made of a two-dimensional stochastic system that models the spread of an infectious disease in a population. An asymptotic expression is derived for the probability that a major outbreak of the disease will occur in case the number of infectives is small. For the case that a major outbreak has occurred, an asymptotic approximation is derived for the expected time that the disease is in the population. The analytical expressions are obtained by asymptotically solving Dirichlet problems based on the Fokker-Planck equation for the stochastic system. Results of numerical calculations for the analytical expressions are compared with simulation results.
对一个二维随机系统进行了研究，该系统模拟了传染病在人群中的传播。在感染人数较少的情况下，推导出了疾病大爆发概率的渐近表达式。对于已经发生大爆发的情况，推导出了疾病在人群中持续时间的期望的渐近近似。通过基于随机系统的福克-普朗克方程渐近求解狄利克雷问题来获得解析表达式。将解析表达式的数值计算结果与模拟结果进行了比较。
