Test students' ability to apply SIR compartmental models and basic calculus to infectious disease control: formulate and analyze SIR differential equations; compute the basic reproduction number R0 and derive the critical vaccination coverage (including effects of imperfect vaccine efficacy); use derivatives, integrals, and phase-plane reasoning to interpret epidemic curves; perform simple stability or sensitivity analyses and evaluate numerical scenarios to recommend vaccination timing and coverage as outbreak control strategies. Assess mathematical setup, computations, graphical interpretation, and justified public-health recommendations.