This paper introduces an optimal control strategy for cholera’s crossover mathematical model. The proposed model integrates Ψ-Caputo fractal variable-order derivatives, fractal fractional-order derivatives, and integer-order derivatives across three distinct time intervals, utilizing a simple non-standard kernel function Ψ(t). A comprehensive stability analysis of the model’s steady states is conducted. The model’s results are compared with real-world data from the cholera outbreak in Yemen. Following this, an optimal control problem is formulated within the crossover framework. To numerically solve the resulting optimality system, a discretized non-standard -finite difference method is developed. Numerical simulations and comparative studies are presented to demonstrate the method’s applicability and the efficiency of the approximation approach. The key finding of this study highlights that the crossover-controlled system proves to be the most effective approach for mitigating and controlling the spread of cholera

The authors have declared no competing interest.

The author(s) received no specific funding for this work.

I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained.

Yes

The details of the IRB/oversight body that provided approval or exemption for the research described are given below:

yes

I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals.

Yes

I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance).

Yes

I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable.

Yes

All relevant data are within the manuscript and its Supporting Information files.