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Measles disease spread and control via vaccination and treatment: A mathematical framework

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  • Zakirullah,

Abstract

In this paper, we consider a mathematical model for measles. Measles remains a significant concern for global public health, as a single case can lead to the infection of 12 to 18 individuals. Therefore, it is vital to provide control interventions and conceptualize the transmission of measles infection. Parameters of the model are fitted using the nonlinear least squares method. The findings highlight the force of infection rate β as the primary driver behind the variation in measles cases. Furthermore, the analysis revealed that parameter ρ emerged as a key factor contributing to the reduction of measles prevalence. The dynamics of measles are conceptualized with an epidemic model with vaccination and treatment factors. The analysis confirms the existence, uniqueness, and positivity of solutions, provides equilibrium states, and yields the effective reproduction threshold. Moreover, the Bayesian Markov Chain Monte Carlo approach is employed to estimate the model parameters and plot the reproduction threshold. The dynamical behavior of the model is studied through a stability analysis. Using the linearization method, a local stability analysis shows R0<1. The Lyapunov functions determine the stability of persistent-infection equilibrium points, ensuring global stability when R0>1. Parameter sensitivities were quantified using PRCC, a standard technique in global sensitivity analysis. The model is numerically solved using the Homotopy Perturbation Method.

Suggested Citation

  • Zakirullah,, 2026. "Measles disease spread and control via vaccination and treatment: A mathematical framework," Chaos, Solitons & Fractals, Elsevier, vol. 203(C).
    • Handle: RePEc:eee:chsofr:v:203:y:2026:i:c:s0960077925017163
    DOI: 10.1016/j.chaos.2025.117703
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    References listed on IDEAS

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    1. Haileyesus Tessema Alemneh & Asnakew Mesele Belay & Fahad Al Basir, 2023. "Modelling, Analysis, and Simulation of Measles Disease Transmission Dynamics," Discrete Dynamics in Nature and Society, Hindawi, vol. 2023, pages 1-20, January.
    2. Md Rafiul Islam & Angela Peace & Daniel Medina & Tamer Oraby, 2020. "Integer Versus Fractional Order SEIR Deterministic and Stochastic Models of Measles," IJERPH, MDPI, vol. 17(6), pages 1-19, March.
    3. Qureshi, Sania & Jan, Rashid, 2021. "Modeling of measles epidemic with optimized fractional order under Caputo differential operator," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
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