Magalang, Juan Antonio (2024). Stochastic Models of Drug Resistance Development. (Thesis). Universität Bern, Bern
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24magalang_ja.pdf - Thesis Available under License Creative Commons: Attribution (CC-BY 4.0). Download (13MB) | Preview |
Abstract
Antimicrobial resistance is a growing threat to public health as therapies designed to treat pathogenic infections lose their efficacy over time. This loss in the efficacy is due to pathogenic evolution which is inherently stochastic. Hence, estimating the times at which pathogens will develop drug resistances is an important quantity to study since it is equivalent to the time that a therapy will fail. Common strategies to mitigate drug resistance development are combination therapies, where two or more therapies are administered simultaneously, and therapy switching, where therapies are replaced or cycled out. This thesis aims to develop a model of drug resistance development within a patient infected with a chronic infection by modelling the within-host infection rate as a bounded and multidimensional Brownian motion with stochastic resetting. Features of this stochastic process reflect therapy administration strategies: multidimensionality represents combination therapies, while stochastic resetting, where a stochastic process returns to its initial position at random times, represents therapy switching. The boundaries of the model are either reflecting or absorbing. Reflecting boundaries prohibit the full recovery of the host as it is under chronic infection, while absorbing boundaries signify the failure of the therapy. The times at which the stochastic process reaches the absorbing boundary is of interest as this also symbolizes the time that drug resistance has emerged. Two scenarios will also be studied in detail: single therapy and multiple therapy protocols. In single therapy protocols, the analytical probability distribution of the resistance development time will be derived in Laplace space, and novel methods in approximating its inversion and in obtaining simulated values with a controllable error. In multiple therapy protocols, analogous stochastic processes will be proposed that are optimized for either combination therapy or therapy switching. This will allow for a thorough investigation of optimal choices of the number of therapies and switching rates, and also the imposition of constraints in terms of the maximum allowed switching rate, total number of therapies available, and costed therapy switching.
| Item Type: | Thesis |
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| Dissertation Type: | Cumulative |
| Date of Defense: | 13 December 2024 |
| Subjects: | 500 Science > 510 Mathematics 600 Technology > 610 Medicine & health |
| Institute / Center: | 08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
| Depositing User: | Sarah Stalder |
| Date Deposited: | 05 Jun 2025 08:53 |
| Last Modified: | 05 Jun 2025 08:53 |
| URI: | https://boristheses.unibe.ch/id/eprint/6271 |
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