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Dynamics of drug on-drug off models with mutations in morbidostat — Dedicated to the seventieth birthday of Professor Gail Wolkowicz

  • Received: 04 October 2022 Revised: 03 June 2023 Accepted: 20 June 2023 Published: 29 June 2023
  • MSC : 34C, 92B, 94D

  • The morbidostat is a bacteria culture device that progressively increases antibiotic drug concentration. It is used to study the evolutionary pathway. In this article, we construct mathematical models for the morbidostat. First we consider the case of no mutations, we study limiting systems and obtain criteria for the large time behavior of the solutions. From the theoretical results and numerical simulations, we conclude that there are two competitive exclusion states of either wild type or mutant type as the threshold parameter $ U $ varies. There are three cases, wild type bacteria excludes all mutants; a mutant dominates in the competition; oscillation between the above two states.

    Next we study the systems of forward mutations and forward-backward mutations. Then we apply a result of pertubation for globally stable state.

    Citation: Ziran Cheng, Sze-Bi Hsu. Dynamics of drug on-drug off models with mutations in morbidostat — Dedicated to the seventieth birthday of Professor Gail Wolkowicz[J]. AIMS Mathematics, 2023, 8(9): 20815-20840. doi: 10.3934/math.20231061

    Related Papers:

  • The morbidostat is a bacteria culture device that progressively increases antibiotic drug concentration. It is used to study the evolutionary pathway. In this article, we construct mathematical models for the morbidostat. First we consider the case of no mutations, we study limiting systems and obtain criteria for the large time behavior of the solutions. From the theoretical results and numerical simulations, we conclude that there are two competitive exclusion states of either wild type or mutant type as the threshold parameter $ U $ varies. There are three cases, wild type bacteria excludes all mutants; a mutant dominates in the competition; oscillation between the above two states.

    Next we study the systems of forward mutations and forward-backward mutations. Then we apply a result of pertubation for globally stable state.



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  • © 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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