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Mathematical model of biofilm-mediated pathogen persistence in a water distribution network with time-constant flows

Published online by Cambridge University Press:  06 June 2018

SADIQAH AL MARZOOQ ,
ALVARO ORTIZ-LUGO  and
BENJAMIN L. VAUGHAN Jr.
SADIQAH AL MARZOOQ
Affiliation:
Department of Mathematical Sciences, McMicken College of Arts and Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA emails: s_almarzooq@yu.edu.sa, ortizlaa@mail.uc.edu, vaughabn@ucmail.uc.edu Al Yamamah University, P.O. Box 45180, Riyadh 11512, Saudi Arabia
ALVARO ORTIZ-LUGO
Affiliation:
Department of Mathematical Sciences, McMicken College of Arts and Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA emails: s_almarzooq@yu.edu.sa, ortizlaa@mail.uc.edu, vaughabn@ucmail.uc.edu
BENJAMIN L. VAUGHAN Jr.
Affiliation:
Department of Mathematical Sciences, McMicken College of Arts and Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025, USA emails: s_almarzooq@yu.edu.sa, ortizlaa@mail.uc.edu, vaughabn@ucmail.uc.edu
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Abstract

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In industrialized nations, potable water is often provided through sophisticated water distribution systems. If pathogenic bacteria are introduced into the water distribution network, the presence of a biofilm can lead to biofilm-assisted retention of the pathogens, affecting the potability of the water. To study the dynamics of planktonic and biofilm-bound pathogens within the large network of pipes in a water distribution system, we develop a network model governing the concentration of introduced pathogens within the bulk fluid and the biofilms lining the pipes. Under time-constant flow regimes within the network, we prove that the long-time behaviour of the entire network is dependent on the Lyapunov exponents for each connection in the network when viewed in isolation and the network connectivity. An efficient algorithm is developed for predicting the long-time behaviour of the pathogen population within large networks using the network's topological ordering. The algorithm's predictions are validated using numerical simulations of the full non-linear system on a range of water distribution network sizes.

Keywords

05C20 directed graphs34D20 stability92B05 general biology and biomathematics92D99 biology and other natural sciences
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 6: Biofilms , December 2018 , pp. 991 - 1019
Copyright
Copyright © Cambridge University Press 2018 

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