Stability and persistence analysis on the epidemic model multiregion multi-patches

Spread of the virus can also occur between cities, countries and continents including the spread of H1N1 pandemic in 2009, the virus H7N9 that once plagued the plains of China, Virus Ebolla 2014 outbreak in the peninsula mainland West Africa, In this paper Mathematical model is constructed based on Metapopulation in 2 Region are connected by three tracks that do not intersect, therefore displacement individually in each region will not move trajectory, movement of individual populations between the Region is influenced by the density function Kernel Exponential and Laplace so Model Metapopulation shaped Equation System differential Partial-Integral loading the second region, stability and persistence analysis conducted through the basic reproduction number and Lipschitz constant showed that the analysis so that the system can be done through a model of each region's to subsystem and system stability and persistence of the population affected by the virus and infected susceptible to the limited and quite large.