In this study, we analyze a fractional \(\mathcal {SIR}\) model with Crowley-Martin incidence rate with time delay, and Holling type-II treatment rate. The model has two equilibria, disease-free and endemic, and their stability is determined by the basic reproduction number \({\mathcal {R}}_0\) . We also discuss the global stability of the model. The study provides insights into the dynamics of infectious diseases and can inform public health policies and interventions for disease control. The incorporation of Crowley-Martin incidence rate and Holling type-II treatment rate allows for a more realistic representation of disease dynamics and treatment impact. Overall, this study contributes to our understanding of infectious disease dynamics in a fractional framework with time delay and treatment rate considerations. We finish this work by giving numerical simulation to illustrate our results.
