Mesüm, Oğuz and Atılgan, Ali Rana and Kocuk, Burak
(2024)
*A stochastic programming approach to the antibiotics time machine problem.*
Mathematical Biosciences, 372
.
ISSN 0025-5564 (Print) 1879-3134 (Online)

Official URL: https://dx.doi.org/10.1016/j.mbs.2024.109191

## Abstract

Antibiotics Time Machine is an important problem to understand antibiotic resistance and how it can be reversed. Mathematically, it can be modeled as follows: Consider a set of genotypes, each of which contain a set of mutated and unmutated genes. Suppose that a set of growth rate measurements of each genotype under a set of antibiotics is given. The transition probabilities of a ‘realization’ of a Markov chain associated with each arc under each antibiotic are computable via a predefined function given the growth rate realizations. The aim is to maximize the expected probability of reaching to the genotype with all unmutated genes given the initial genotype in a predetermined number of transitions, considering the following two sources of uncertainties: (i) the randomness in growth rates, (ii) the randomness in transition probabilities, which are functions of growth rates. We develop stochastic mixed-integer linear programming and dynamic programming approaches to solve static and dynamic versions of the Antibiotics Time Machine Problem under the aforementioned uncertainties. We adapt a Sample Average Approximation approach that exploits the special structure of the problem and provide accurate solutions that perform very well in an out-of-sample analysis.

Item Type: | Article |
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Uncontrolled Keywords: | Bacterial growth rate; Beta-lactamase; Drug delivery; Dynamic programming; Fitness landscape; Mixed-integer linear programming |

Divisions: | Faculty of Engineering and Natural Sciences |

Depositing User: | Ali Rana Atılgan |

Date Deposited: | 10 Jun 2024 13:21 |

Last Modified: | 10 Jun 2024 13:21 |

URI: | https://research.sabanciuniv.edu/id/eprint/49325 |