Heterogeneity in multiple transmission pathways: modelling the spread of cholera and other waterborne disease in networks with a common water source

Abstract

Many factors influencing disease transmission vary throughout and across populations. For diseases spread through multiple transmission pathways, sources of variation may affect each transmission pathway differently. In this paper we consider a disease that can be spread via direct and indirect transmission, such as the waterborne disease cholera. Specifically, we consider a system of multiple patches with direct transmission occurring entirely within patch and indirect transmission via a single shared water source. We investigate the effect of heterogeneity in dual transmission pathways on the spread of the disease. We first present a 2-patch model for which we examine the effect of variation in each pathway separately and propose a measure of heterogeneity that incorporates both transmission mechanisms and is predictive of R₀. We also explore how heterogeneity affects the final outbreak size and the efficacy of intervention measures. We conclude by extending several results to a more general n-patch setting.

Keywords:

• epidemiology
• heterogeneity
• cholera
• basic reproduction number
• network
• multiple transmission pathways

Acknowledgements

We thank Tony Nance for his advice and discussion on this work.

Funding

This work was supported by the National Science Foundation through the Mathematical Biosciences Institute (DMS 0931642) and Grant OCE-1115881.