Mathematical Modelling and Optimal Control of Measles Epidemics: A Review of Compartmental, Fractional, Stochastic and Spatial Approaches

The literature on mathematical modelling of measles has developed from classical deterministic SEIR models to more advanced frameworks incorporating vaccination, multiple vaccine doses, waning immunity, stochastic effects, fractional calculus, spatial heterogeneity and optimal control. From a mathematical perspective, the most important components of a measles model are: Model Formulation → Equilibrium Analysis → R0 → Stability → Sensitivity Analysis → Numerical Solution → Optimal Control The existing literature provides a strong foundation, but a significant research gap remains in developing an integrated model that combines vaccination, waning immunity, spatial heterogeneity, advanced mathematical dynamics and optimal control. Therefore, future research should focus on developing mathematically rigorous and computationally efficient measles models that can provide both theoretical insights and practical guidance for epidemic control.

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