# Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens

Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens Humans are often colonized by polymorphic bacteria such as Streptococcus pneumoniae, Bordetella pertussis, Staphylococcus Aureus, and Haemophilus influenzae. Two co-colonizing pathogen clones may interact with each other upon host entry and during within-host dynamics, ranging from competition to facilitation. Here we examine the significance of these exploitation strategies for bacterial spread and persistence in host populations. We model SIS epidemiological dynamics to capture the global behavior of such multi-strain systems, focusing on different parameters of single and dual colonization. We analyze the impact of heterogeneity in clearance and transmission rates of single and dual colonization and find the criteria under which these asymmetries enhance endemic persistence. We obtain a backward bifurcation near $$R_0 = 1$$ R 0 = 1 if the reproductive value of the parasite in dually infected hosts is sufficiently higher than that in singly infected ones. In such cases, the parasite is able to persist even in sub-threshold conditions, and reducing the basic reproduction number below 1 would be insufficient for elimination. The fitness superiority in co-colonized hosts can be attained by lowering net parasite clearance rate ( $$\gamma _\mathrm{{d}}$$ γ d ), by increasing transmission rate ( $$\beta _\mathrm{{d}}$$ β d ), or both, and coupling between these traits critically constrains opportunities of pathogen survival in the $$R_0<1$$ R 0 < 1 regime. Finally, using an adaptive dynamics approach, we verify that despite their importance for sub-threshold endemicity, traits expressed exclusively in coinfection should generally evolve independently of single infection traits. In particular, for $$\beta _\mathrm{{d}}$$ β d a saturating parabolic or hyperbolic function of $$\gamma _\mathrm{{d}}$$ γ d , co-colonization traits evolve to an intermediate optimum (evolutionarily stable strategy, ESS), determined only by host lifespan and the trade-off parameters linking $$\beta _\mathrm{{d}}$$ β d and $$\gamma _\mathrm{{d}}$$ γ d . Our study invites more empirical attention to the dynamics and evolution of parasite life-history traits expressed exclusively in coinfection. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of Mathematical Biology Springer Journals

# Transmission Fitness in Co-colonization and the Persistence of Bacterial Pathogens

, Volume 79 (9) – Jul 24, 2017
20 pages

/lp/springer_journal/transmission-fitness-in-co-colonization-and-the-persistence-of-9zqcDuyWzR
Publisher
Springer US
Subject
Mathematics; Mathematical and Computational Biology; Life Sciences, general; Cell Biology
ISSN
0092-8240
eISSN
1522-9602
D.O.I.
10.1007/s11538-017-0320-3
Publisher site
See Article on Publisher Site

### Abstract

Humans are often colonized by polymorphic bacteria such as Streptococcus pneumoniae, Bordetella pertussis, Staphylococcus Aureus, and Haemophilus influenzae. Two co-colonizing pathogen clones may interact with each other upon host entry and during within-host dynamics, ranging from competition to facilitation. Here we examine the significance of these exploitation strategies for bacterial spread and persistence in host populations. We model SIS epidemiological dynamics to capture the global behavior of such multi-strain systems, focusing on different parameters of single and dual colonization. We analyze the impact of heterogeneity in clearance and transmission rates of single and dual colonization and find the criteria under which these asymmetries enhance endemic persistence. We obtain a backward bifurcation near $$R_0 = 1$$ R 0 = 1 if the reproductive value of the parasite in dually infected hosts is sufficiently higher than that in singly infected ones. In such cases, the parasite is able to persist even in sub-threshold conditions, and reducing the basic reproduction number below 1 would be insufficient for elimination. The fitness superiority in co-colonized hosts can be attained by lowering net parasite clearance rate ( $$\gamma _\mathrm{{d}}$$ γ d ), by increasing transmission rate ( $$\beta _\mathrm{{d}}$$ β d ), or both, and coupling between these traits critically constrains opportunities of pathogen survival in the $$R_0<1$$ R 0 < 1 regime. Finally, using an adaptive dynamics approach, we verify that despite their importance for sub-threshold endemicity, traits expressed exclusively in coinfection should generally evolve independently of single infection traits. In particular, for $$\beta _\mathrm{{d}}$$ β d a saturating parabolic or hyperbolic function of $$\gamma _\mathrm{{d}}$$ γ d , co-colonization traits evolve to an intermediate optimum (evolutionarily stable strategy, ESS), determined only by host lifespan and the trade-off parameters linking $$\beta _\mathrm{{d}}$$ β d and $$\gamma _\mathrm{{d}}$$ γ d . Our study invites more empirical attention to the dynamics and evolution of parasite life-history traits expressed exclusively in coinfection.

### Journal

Bulletin of Mathematical BiologySpringer Journals

Published: Jul 24, 2017

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