这里构造了混合状态空间中的不变集，证明了系统在HDS意义下的渐近稳定性。

Invariant sets of HDS are constructed in hybrid state space, and then the system's asymptotic stability is proved in the sense of HDS.

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通过构造 函数及根据 不变集原理证明了无病平衡点和地方病平衡点的全局渐近稳定性；

Then the disease-free equilibrium point and endemic equilibrium point were proved with global asymptotic stability by constructing functions and basing on the invariant set principle.

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为了得到关于弱集值渐近鞅的收敛性质，首先证明了支撑函数列的极限亦为一支撑函数。

In order to get the convergence properties of the weak set-valued Amart, we firstly proved the theorem that the limit of support functions is a support function.

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