Binomial and Stochastic Transmission Models

Abstract

How we think about the transmission dynamics of an infectious agent within a host population influences how we design, analyze, and interpret vaccine studies. It can influence our choice of interventions. In this chapter and the next we introduce transmission models necessary for estimating and understanding the effects of vaccination. In this chapter, we present the binomial model and the chain binomial model. These models are central to formulating statistical models for estimating transmission parameters and vaccine efficacy parameters. They form the basis of the models in Chapters 10 through 12. The binomial model is also the basic building block of the small- and large-scale stochastic simulation models of vaccination interventions in populations, that can also be used to produce data for design of vaccine studies. In a stochastic model, whether an event occurs is random, depending on a number produced by a random number generator described later.

In Chapter 5 we present simple differential equation transmission models that are generally deterministic. That is, every time the equations are solved, the same answer is obtained. This approach is essential to understanding large complex models of the population effects of vaccination programs, but less relevant to our purposes in this book. Much of theoretical discussion of the effect of vaccination on the basic reproductive number R₀ stems from the solution of differential equation m odels, so the chapter discusses R₀ and the effects of vaccination.