Sensitivity analysis of a branching process evolving on a network with application in epidemiology

TL;DR

This paper conducts an analytical sensitivity analysis of a network-based branching process model, applied to early-stage influenza epidemics, revealing key parameters influencing epidemic growth and vaccination impact.

Contribution

It introduces an analytical sensitivity analysis framework for branching processes on networks and applies it to epidemiology, highlighting parameter importance and vaccination effects.

Findings

Epidemic growth is more sensitive to within-city transmission rates.

Travel rates between cities have less impact on epidemic growth.

Sensitivity analysis provides practical insights for epidemic control strategies.

Abstract

We perform an analytical sensitivity analysis for a model of a continuous-time branching process evolving on a fixed network. This allows us to determine the relative importance of the model parameters to the growth of the population on the network. We then apply our results to the early stages of an influenza-like epidemic spreading among a set of cities connected by air routes in the United States. We also consider vaccination and analyze the sensitivity of the total size of the epidemic with respect to the fraction of vaccinated people. Our analysis shows that the epidemic growth is more sensitive with respect to transmission rates within cities than travel rates between cities. More generally, we highlight the fact that branching processes offer a powerful stochastic modeling tool with analytical formulas for sensitivity which are easy to use in practice.