NDLI: Stability Analysis of Population Dynamics Model in Microbial Biofilms with Non-participating Strains

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Stability Analysis of Population Dynamics Model in Microbial Biofilms with Non-participating Strains

Content Provider	ACM Digital Library
Author	Banerjee, Jeet Layek, Ritwik Kumar Ranjan, Tanvi
Abstract	The existence of phenotypic heterogeneity in single-species bacterial biofilms is well-established in the published literature. However, the modeling of population dynamics in biofilms from the viewpoint of social interactions, i.e. interplay between heterotypic strains, and the analysis of this kind using control theory are not addressed significantly. Therefore, in this paper, we theoretically analyze the population dynamics model in microbial biofilms with non-participating strains (coexisting with public goods producers and non-producers) in the context of evolutionary game theory and nonlinear dynamics. Our analysis of the replicator dynamics model is twofold: first without the inclusion of spatial pattern, and second with the consideration of degree of assortment. In the first case, Lyapunov stability analysis of the stable equilibrium point of the proposed replicator system determines (1,0) ('full dominance of cooperators') as a global asymptotic stable equilibrium whenever the return exceeds the metabolic cost of cooperation. Hence, the global asymptotic stable nature of (1,0) in the context of non-consideration of spatial pattern helps to justify mathematically the adversity in the eradication of "cooperative enterprise" that is an infectious biofilm. In the second case, we found non-existence of global asymptotic stability in the system, and it unveils two additional phenomena - bistability and coexistence. In this context, two inequality conditions are derived for the 'full dominance of cooperators' and coexistence. Therefore, the inclusion of spatial pattern in biofilms with non-competing strains intends conditional dominance of pathogenic (with respect to the hosts) public goods producers which can be an effective strategy towards the control of an infectious biofilm with the drug-dependent regulation of degree of segregation. Furthermore, the simulation results of the proposed dynamics for both the discussed scenario confirm the results of the analysis of equilibrium points. The proposed stability analysis not only demonstrate a mathematical framework to analyze the population dynamics in biofilms but also gives a clue to control an infectious biofilm, where phenotypic and spatial heterogeneity exist.
Starting Page	220
Ending Page	230
Page Count	11
File Format	PDF
ISBN	9781450342254
DOI	10.1145/2975167.2975190
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2016-10-02
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Nonlinear dynamics Social interactions Biofilm Population dynamics Spatial pattern Public goods Evolutionary game theory
Content Type	Text
Resource Type	Article

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