Analyzing the Impact of Mass Vaccination on Disease Spread: A Stochastic Perspective

Abstract

This work adopts a stochastic approach to analyze the impact of mass vaccination on the spread of an epidemiological disease. The number of individuals each infected person can transmit the disease to, referred to as contagion, is modeled as a discrete random variable following a binomial distribution. The progression of infections over time is represented by a stochastic branching process. The primary goal is to investigate how the percentage of vaccinated individuals and the efficacy of the vaccine affect both the spread of the disease and the probability of extinction. The analysis is based on sample statistics such as the mean and variance of the number of infections over time, as well as histograms of their distributions. The statistical models are constructed using Monte Carlo simulations under various scenarios combining different levels of vaccine coverage, efficacy, and contagion parameters. Specifically, six levels of vaccinated population percentage, four values for vaccine efficacy, and 21 different parameter sets for the binomial contagion distribution are considered. For each scenario, 4000 realizations of the branching process were simulated, totaling 2.1 million realizations. This scale of data characterizes the study as a big data problem.