Abstract
<title>Abstract</title> <p>Mpox, an emerging zoonotic disease, presents significant public health concerns due to its capacity for animal-to-human spillover and sustained human-to-human transmission. This paper develops a coupled SVEIQR-SEI mathematical framework capturing transmission dynamics between animal reservoirs and human populations, incorporating vaccination and quarantine interventions. Mathematical analysis establishes the basic reproduction number (R0 = max{Rr, Rh}), proving that the disease-free equilibrium is locally asymptotically stable when R0 < 1. Furthermore, Castillo-Chavez and Song's center manifold theory demonstrates a forward bifurcation at R0 = 1, confirming disease elimination is feasible without bistability concerns. A global Partial Rank Correlation Coefficient (PRCC) sensitivity analysis over 240 days reveals that human-to-human transmission dominates early outbreak phases, while reservoir dynamics become highly influential during peak and decline phases. To evaluate real-world applicability, the model was risk-stratified and heuristically calibrated to the 2022 United States Mpox outbreak. The optimized model achieved exceptional fit to the epidemic curve (R2 = 0.985), demonstrating that targeted quarantine and behavioral interventions within high-risk networks were the primary drivers of outbreak containment. Ultimately, these results emphasize the necessity of adaptive, phase-specific control strategies targeting both human networks and animal hosts.</p>