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Bains, Karan Partap

University of British Columbia

The toxic drug overdose crisis has continued to be a major problem in British Columbia, with approximately 6− 7 people dying each day, on average, because of drug overdoses. We formulated several mathematical models to gain a quantitative understanding of the experiences of people who use opioids in British Columbia. These models include compartmental ODE models and age-structured PDE models. The models that we developed allowed us to answer questions at an individual level, such as the average number of overdoses experienced by a person over time. We studied how the average number of overdoses depends on the parameters of the compartmental ODE models. We determined a mathematical relationship between the relapse rate, treatment rate, and the average number of overdoses in a person in their lifetime. At the population level, we used numerical simulations to investigate the effects of different relapse and treatment rates on the number of people who use opioids over time. We generated stochastic simulations using the Gillespie algorithm to discretize the death and overdose events, and the transitions between compartments from the ODE models. With the age-structured PDE models, we studied the impact of mandatory treatment on population dynamics and the average number of overdoses experienced by a person over time. Our findings indicate that the implementation of mandatory treatment is correlated with a decrease in the average number of overdoses experienced by a person over time. In the future, individual-based data on the times spent by people in treatment or the time before relapse can be incorporated into our age-structured models to model the relapse rate more realistically.

Text

2024-12-19

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/89949

Mathematics

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/