The discrete fractional order difference applied to an epidemic model with indirect transmission

• We propose a discrete fractional order model to analyze the behaviour of an epidemic process with indirect transmission. Our main contribution is study influence and memory steps on solution. The stability around equilibrium points our analyzed. obtain some bounds tan introduction derivhe population size assure nonnegativity solution model. A proposed This based version Grunwald-Letnikov derivative operator. Some properties this operator are shown used derive truncated operator, which short-term memory. Based biological meaning problem, have been obtained ( ? , k ) -Basic Reproduction Number has introduced its points. Moreover, order, steps, Finally, results clarified by means numerical simulations for evolution infection Salmonella in hens farm.