Hybrid artificial intelligence framework for deterministic and stochastic modelling of skin sores disease with optimal control analysis

Impetigo is a major cause of childhood morbidity in remote and resource-limited communities, where mass treatment rather than vaccination is the operative public-health lever. We formulate a four-compartment deterministic model extending existing formulations by two treatment parameters: decolonisation of exposed individuals and antibiotic treatment of active lesions. The model is positively invariant and uniformly bounded, and the disease-free equilibrium is shown to be locally and globally asymptotically stable when the basic reproduction number is below unity. Sensitivity analysis identifies treatment of active lesions as the most influential controllable parameter (elasticity −0.691). An Itô stochastic extension admits a unique global positive solution, and an extinction threshold shows that large environmental fluctuation can eradicate infection even when the deterministic reproduction number exceeds unity. With vaccination and both treatment rates as time-dependent controls, Pontryagin's Maximum Principle with a forward–backward sweep reduces the cost functional by 93.3% and cumulative infections by 97.0% over 200 days, the optimal effort being strongly front-loaded. Feedforward neural networks provide accurate deterministic and distributional surrogates, and recover parameters from noisy weekly case counts under deterministic dynamics (R 2 ≈ 0.89) but only weakly from a single stochastic realisation (R 2 = 0.36), indicating that single-community surveillance cannot identify transmission. Treatment of active lesions, not vaccination, is the dominant lever.

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