In a controlled exposure study, two cohorts each of 100 volunteers were exposed to different doses of a respiratory virus. Cohort A (low dose) had 12 infections; Cohort B (high dose) had 72 infections. Calculate the fold-increase in infection probability from low to high dose and interpret what this implies about dose-dependence.

For a pathogen with R0 = 3.0, what herd immunity threshold (proportion immune) is required to prevent sustained transmission in a fully susceptible population (assume perfect vaccine efficacy)?

Given a pathogen with moderate R0 = 2.5 that peaks seasonally in late autumn due to indoor crowding, synthesize an optimal vaccination timing strategy and target coverage to minimize peak transmission in the upcoming season (assume vaccine efficacy 85%).

Design the most effective surveillance strategy to detect antigenic changes in circulating influenza strains that could undermine vaccine effectiveness. Which combination of activities would be best?

A nursing home reports low influenza vaccine uptake among staff and residents followed by an outbreak. Which immediate actions best reduce further transmission and protect unvaccinated and immunocompromised residents?