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Mathematical Simulation of Optimal Control Measures to Avoid Chickenpox Infection

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  • Nada A. Almuallem
  • Hegagi Mohamed Ali
  • Essam M. Elsaid
  • Mohamed R. Eid
  • W. S. Hassanin

Abstract

This work presents a comprehensive mathematical analysis of the chickenpox transmission model, including positivity, existence, invariant region, and uniqueness of the solution. We enhance the model by introducing optimal control measures using two time‐dependent control variables: prevention measures like vaccination and movement constraints, and isolation measures like quarantine. The study evaluates the basic reproduction number R0, equilibrium points, and stability. New contributions include the analysis of the model’s bifurcations and the proof of the existence of optimal control using Fleming’s theorem. Numerical simulations demonstrate the effectiveness of optimal control strategies in reducing infection. These results highlight the practical importance of the proposed model in mitigating chickenpox outbreaks and provide a basis for future extensions to fractional systems and additional control variables. The results led us to conclude that, to reduce the danger of catching the chickenpox virus, it is imperative to apply suggested control measures.

Suggested Citation

  • Nada A. Almuallem & Hegagi Mohamed Ali & Essam M. Elsaid & Mohamed R. Eid & W. S. Hassanin, 2025. "Mathematical Simulation of Optimal Control Measures to Avoid Chickenpox Infection," International Journal of Mathematics and Mathematical Sciences, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jijmms:v:2025:y:2025:i:1:n:3238188
    DOI: 10.1155/ijmm/3238188
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    References listed on IDEAS

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    1. Bashier, Eihab B.M. & Patidar, Kailash C., 2017. "Optimal control of an epidemiological model with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 47-56.
    2. Jana, Soovoojeet & Haldar, Palash & Kar, T.K., 2016. "Optimal control and stability analysis of an epidemic model with population dispersal," Chaos, Solitons & Fractals, Elsevier, vol. 83(C), pages 67-81.
    3. Kar, T.K. & Nandi, Swapan Kumar & Jana, Soovoojeet & Mandal, Manotosh, 2019. "Stability and bifurcation analysis of an epidemic model with the effect of media," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 188-199.
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