On the Mathematical Modelling of a Bacteria Behaviour Using Reaction Schemes

Authors

  • Rene Alt* Universite Pierre et Marie Curie
  • Margarita Kambourova
  • Nadja Radchenkova Institute of Microbiology, Bulgarian Academy of Sciences
  • Spasen Vassilev Institute of Microbiology, Bulgarian Academy of Sciences
  • Svetoslav Markov

DOI:

https://doi.org/10.11145/314

Abstract

Trying to find a mathematical model explaining the behaviour of a biological process is a difficult challenge when one only has someВ  experimental measures of few parameters concerning this process. In this work we are interested in mathematical models for the production of exopolysaccharide (EPS). by aeribacillus placidus. Several experiments [2], have shown that this production begins with a long period (several hours) in which the biomass and EPS remain undetectable. Then there is a fast increase followed by a stationary situation or a slow decrease of the biomass and EPS. Some differential models have already been proposed such that their computed solution stay in the interval error of the experimental measures. Here we are interested in two particular models arising from reaction schemes consisting of two phases, mainly a non-reproductive phase and a reproductive phase, in the life of a bacteria. This approach has been proposed in [1]. It is shown that both models,even if they have different hypotheses lead to theoretical solutions that very close to the experiments whereas the Andrews-Haldane model can not fit well the first hours of the process. Then some interesting mathematical properties of these two models are studied. Numerical simulations coming from these models are presented.

Author Biographies

Margarita Kambourova

Institute of Microbiology, Bulgarian Academy of Sciences

Svetoslav Markov

Instite of Mathematics and Informatics, Bulgarian Academy of Sciences

Downloads

Published

2014-04-28

Issue

Vol. 1 No. 1 (2014)

Section

Conference Contributions

License

The journal Biomath Communications is an open access journal. All published articles are immeditely available online and the respective DOI link activated. All articles can be access for free and no reader registration of any sort is required. No fees are charged to authors for article submission or processing. Online publications are funded through volunteer work, donations and grants.

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).