一类具有潜伏期和染病年龄的SEIR传染病模型

A Class of SEIR Epidemic Model with Latent Period and Infectious Age

研究了一类具有潜伏期和染病年龄的SEIR传染病模型,利用特征线法、积分方程理论和Banach不动点定理证明了该模型局部解的存在唯一性,通过先验估计证明了整体解的存在唯一性,并利用Gronwall不等式证明了解对初值的连续依赖性.最后,讨论了解的正则性.

The paper researches a class of SEIR epidemic model with infectious age and latent period. The existence uniqueness of local solution is proved by using characteristic method, the theories of integrate equation and Banach fixed point theorem. Then the existence uniqueness of global solution and continuous dependence of solutions for initial value is obtained by prior estimation and Gronwall inequality. In the end, the regularity of solution is discussed.