Modeling the transmission dynamics of Mpox virus.

The global emergence of human monkeypox (Mpox) necessitates stage-structured transmission models. We develop a compartmental framework with Prodromal, Rash, and Complication stages, identifying critical thresholds through bifurcation analysis. A transcritical bifurcation at [Formula: see text] day[Formula: see text] separates stable disease-free equilibrium ([Formula: see text]) from endemic spread. Normalized sensitivity analysis establishes transmission rate β ([Formula: see text]) as the dominant epidemic driver, with mortality μ ([Formula: see text]) and progression rate [Formula: see text] ([Formula: see text]) as key modulators. Intervention analysis reveals: (1) 22.7% outbreak reduction (95% CI: 19.4-25.1%) through prodromal case isolation (days 0-5) requiring 92% diagnostic accuracy; (2) Linear [Formula: see text] response to transmission controls (0.0398 reduction per 10% β decrease); (3) Phase-adaptive resource allocation (60% to transmission reduction) sustains subcritical operation. The framework advocates real-time β monitoring via wastewater surveillance and [Formula: see text]-optimized diagnostics.