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This article shows epidemic model, earlier suggested in ordinary differential equation philosophy, can be extended to fractional order on a reliable agenda of biological comportment. A set of domains for the model wherein allvariables are limited is established. Furthermore, the stability and existence of steadiness points are studied. We present the evidence that the endemic equilibrium (EE) point is locally asymptotically stable when reproduction number R 0 > 1. This outcome is attained via the linearization statement for fractional differential equations (FDEs). The worldwide asymptotic stability of a disease-free point, when R 0 < 1, is also verified by comparison theory for fractional differential equations. The numeric replications for diverse consequences are carried out, and data attained are in good agreement with theoretical outcomes, displaying a vital perception about the use of the set of fractional coupled differential equations to model babesiosis disease and tick populations.

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