一类传染病动力学偏微分方程组解的适定性

The Well-posedness of Solutions to PDE Model of Infectious Dynamics

为探讨传染病的发展趋势和规律,以及采取适当的措施预防和控制传染病,最终提高全民的人口素质和生活质量,考虑到人对防治传染病的主观能动性,对一类采取预防隔离措施的非终身免疫型传染病动力学模型进行了讨论,利用特征线方法与压缩不动点定理得到了其解的局部存在唯一性,然后通过作先验估计证明了解的整体存在唯一性,以及解对初值的连续依赖性,其中多次用到了Gronwell不等式,最后通过引入相容性条件讨论了解的光滑性。为用该模型来预测传染病的发展过程提供了理论依据。

Infectious dynamics inspects the influence of infectious disease for population distribution and searches for developing trend and law of infectious disease so that we can take precautions against it and control it by suitable measures and improve population quality and living standard of the whole nation. Considering people＇s subjective efforts for guarding against infections, in this paper, an infectious model with preventive-separated measure is discussed and theory basis is provided for forecasting infectious developing process by using the model. We get local existence uniqueness of the solution by characteristic method and fixed point theorem and prove the whole existence uniqueness of the solution and continuously dependent of solutions for initial value by making use of prior estimation and important Gronwell inequality. In the end, smooth of the solution is discussed.