标题： 一种具有非限制传播的流行病网络非局部模型：全局存在性和唯一性 显示英文标题

标题： A nonlocal model of epidemic network with nonlimited transmission: Global existence and uniqueness

摘要： 根据\cite{ipel1}，我们考虑一个描述网络上流行病传播的非线性 SIS 型非局部系统，假设传播不受限制，我们证明了对于任何扩散系数，解都存在唯一局部解，并在扩散系数相等的情况下证明了全局存在性。 接下来我们研究解的渐近行为，并表明当总平均人口较小时，无病平衡点（DFE）是线性和全局渐近稳定的。 最后，我们证明该系统的解收敛到$DFE$。 显示英文摘要

摘要： Following \cite{ipel1}, we consider a nonlinear SIS-type nonlocal system describing the spread of epidemics on networks, assuming nonlimited transmission, We prove local existence of a unique solution for any diffusion coefficients and global existence in the case of equal diffusion coefficients. Next we study the asymptotic behaviour of the solution and show that the disease-free equilibrium (DFE) is linearly and globally asymptotically stable when the total mean population is small. Finally, we prove that the solution of the system converge to the $DFE$.