Basic stochastic transmission models and their inference

TL;DR

This survey reviews stochastic models of infectious disease spread, focusing on their mathematical properties and statistical inference methods, with applications to vaccination strategies and disease control.

Contribution

It provides a comprehensive overview of stochastic transmission models, including extensions for realism and methods for statistical inference from various data levels.

Findings

Branching process approximation for large populations

Estimation of basic reproduction number R0

Inference methods for vaccination strategy planning

Abstract

The current survey paper concerns stochastic mathematical models for the spread of infectious diseases. It starts with the simplest setting of a homogeneous population in which a transmittable disease spreads during a short outbreak. Assuming a large population some important features are presented: branching process approximation, basic reproduction number $R_0$, and final size of an outbreak. Some extensions towards realism are then discussed: models for endemicity, various heterogeneities, and prior immmunity. The focus is then shifted to statistical inference. What can be estimated for these models for various levels of detailed data and with what precision? The paper ends by describing how the inference results may be used for determining successful vaccination strategies. This paper will appear as a chapter of a forthcoming book entitled \emph{Handbook of Infectious Disease Epidemiology}.