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In this manuscript, we develop existence, uniqueness and stability criteria for fractional order Typhoid fever model having Caputo–Fabrizio operator by using fixed point theory. This approach of the fractional derivative is relatively new for such kind of biological models. We have also obtained the first accessible approximate solutions for a proposed model by utilizing iterative Laplace transform method. This technique is a combination of one of the reliable method known as new iterative method and Laplace transform method. Finally, we have evaluated parameters that portray the conduct of illness and present the numerical simulations using plots.