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arXiv · 1704.02961

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

Elisabeth Logak·Isabelle Passat
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Abstract

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 $DFE$.

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Elisabeth Logak, Isabelle Passat. 2017-04-10. A nonlocal model of epidemic network with nonlimited transmission: Global existence and uniqueness. https://arxiv.org/abs/1704.02961

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