Fractional optimal control strategies for mitigating cholera epidemics: A mathematical modeling approach

Barira  Afzal; Muhammad Umar  Riaz; Mustafa  Habib

doi:10.59400/jam2459

Fractional optimal control strategies for mitigating cholera epidemics: A mathematical modeling approach

Barira Afzal Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan
Muhammad Umar Riaz University of the Punjab, Lahore 54590, Pakistan
Mustafa Habib Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan

Article ID: 2459

DOI: https://doi.org/10.59400/jam2459

Keywords: cholera epidemics; mathematical modeling; fractional optimal control; caputo derivative; SIQRB model; MATLAB

Abstract

The SIQRB model is employed in this research to propose a Caputo-based fractional derivative optimal control model for the mitigation of cholera epidemics. Significant properties of the model, such as the non-negativity and boundedness of the solution, are verified. The basic reproduction number, , is calculated using the spectral radius of the next-generation matrix. The stability analysis demonstrates that the disease-free equilibrium is locally asymptotically stable when , while the endemic equilibrium is stable when . Numerical simulations are conducted using Euler’s method to demonstrate the importance of the control function. These MATLAB-based simulations illustrate the impact of fractional-order derivatives on cholera transmission dynamics and confirm the analytical results. The efficacy of fractional optimal control approaches in mitigating cholera epidemics is demonstrated.

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Published

2025-03-20

How to Cite

Afzal, B., Riaz, M. U., & Habib, M. (2025). Fractional optimal control strategies for mitigating cholera epidemics: A mathematical modeling approach. Journal of AppliedMath, 3(2), 2459. https://doi.org/10.59400/jam2459

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