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In the present work, we consider a mathematical modelling of an SIR epidemic model with S the susceptible, “healthy individuals who can catch the disease”, I the infected, “those who have the disease and can transmit it”, and R the removed “individuals who have had the disease and are now immune to the infection”. We focus on a spatiotemporal distribution of healthy and infected populations. We study the existence of stationary solutions to the problem type SIR through Schauder’s theorem. 

SIR model, dissemination of epidemics, fixed point.