An epidemiologist models a city’s vaccination rollout: 60% of the population must be immune to achieve herd immunity. The city has 2.4 million people. Vaccination efficiency is 90% per dose, meaning only 90% of administered doses confer immunity. How many doses must be administered to reach herd immunity?

Mon, 20 Apr 2026 04:24:33 +0000

How Epidemiologists Calculate Vaccine Doses Needed for Herd Immunity: A Model for a 2.4-Million-Person City Achieving herd immunity is a critical goal during infectious disease outbreaks, and epidemiologists use mathematical modeling to guide public health strategies. One key question is: how many vaccine doses must be administered to reach herd immunity in a city of 2.4 million people—when 60% of the population needs to be immune, and each vaccination dose is only 90% effective? ### Understanding the Herd Immunity Threshold Herd immunity occurs when enough of a population is immune to an infectious disease—either through vaccination or prior infection—so the spread becomes unsustainable. For a given disease, the required percentage of immune individuals depends on the pathogen’s transmissibility, measured by the basic reproduction number (R₀). However, in vaccination planning, public health experts often assume a target herd immunity threshold of 60%.