具有种群间接触和趋避性的传染病传播模型
On a model for epidemic spread with interpopulation contact and repellent taxis
摘要：
我们研究了一个PDE模型的动力学的易感染的相互作用。当它们远离感染的密度增加时，易感染物的扩散是通过扩散和驱避趋性。传染扩散是一个非线性的，可能退化的非发散形式的术语。我们证明了在一维空间中，对于一个正的易感初始种群，存在所谓的弱-强解。对于维数$N\geq 2$和非负敏感初始密度，我们证明了上解的存在性.数值模拟进行了不同的情况下，并说明了时空行为的解决方案。
英文摘要：
We study a PDE model for dynamics of susceptible-infected interactions. The dispersal of susceptibles is via diffusion and repellent taxis as they move away from the increasing density of infected. The diffusion of infected is a nonlinear, possibly degenerating term in nondivergence form. We prove the existence of so-called weak-strong solutions in 1D for a positive susceptible initial population. For dimension $N\geq 2$ and nonnegative susceptible initial density we show the existence of supersolutions. Numerical simulations are performed for different scenarios and illustrate the space-time behaviour of solutions.
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