Abstract
A spatially structured linear model of the growth of intestinal bacteria is analysed from two generational viewpoints. Firstly, the basic reproduction number associated with the bacterial population, i.e. the expected number of daughter cells per bacterium, is given explicitly in terms of biological parameters. Secondly, an alternative quantity is introduced based on the number of bacteria produced within the intestine by one bacterium originally in the external media. The latter depends on the parameters in a simpler way and provides more biological insight than the standard reproduction number, allowing the design of experimental procedures. Both quantities coincide and are equal to one at the extinction threshold, below which the bacterial population becomes extinct. Optimal values of both reproduction numbers are derived assuming parameter trade-offs.
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Acknowledgements
This work has been partially supported by the coordinated Projects MTM2014-52402-C3-2 and MTM2014-52402-C3-3 of the Spanish government. JR is also partially supported by the project MPCUdG2016/047 of the University of Girona and CB by the Spanish Ministry of Education Grant FPU13/04333.
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Barril, C., Calsina, À. & Ripoll, J. On the Reproduction Number of a Gut Microbiota Model. Bull Math Biol 79, 2727–2746 (2017). https://doi.org/10.1007/s11538-017-0352-8
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DOI: https://doi.org/10.1007/s11538-017-0352-8