Journal of Mathematical Biology

, Volume 66, Issue 3, pp 535–546

Role of environmental persistence in pathogen transmission: a mathematical modeling approach


DOI: 10.1007/s00285-012-0520-2

Cite this article as:
Breban, R. J. Math. Biol. (2013) 66: 535. doi:10.1007/s00285-012-0520-2


Although diseases such as influenza, tuberculosis and SARS are transmitted through an environmentally mediated mechanism, most modeling work on these topics is based on the concepts of infectious contact and direct transmission. In this paper we use a paradigm model to show that environmental transmission appears like direct transmission in the case where the pathogen persists little time in the environment. Furthermore, we formulate conditions for the validity of this modeling approximation and we illustrate them numerically for the cases of cholera and influenza. According to our results based on recently published parameter estimates, the direct transmission approximation fails for both cholera and influenza. While environmental transmission is typically chosen over direct transmission in modeling cholera, this is not the case for influenza.


Environmental transmissionEnvironmental persistenceDirect transmissionSlow–fast dynamics

Mathematics Subject Classification (2000)


Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Unité d’Epidémiologie des Maladies EmergentesInstitut PasteurParisFrance