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Summary

Our response to the opioid epidemic has been reactionary, however preventing future addiction saves lives and money. Methods to prevent opioid misuse and addiction are frequently placed in one of three categories: universal, selective, or indicated. Universal prevention addresses an entire group of people without respect to any factors that might predispose someone to addiction. Most school-based curricula and education for prescribers fall under this category. Selective interventions are geared towards a subset of a population indentified as a higher risk for opioid use disorder, for example programs developed for children who have experienced traumatic events. Finally, indicated prevention focuses on individuals who are already using opioids but do not yet meet criteria for a clinical diagnosis of opioid use disorder. No matter the type, all strategies have the potential to postiively impact individuals and communities through reduced rates of addiction, overdose, and death.

We aim at characterizing viability, invariance and some reachability properties of controlled piecewise deterministic Markov processes (PDMPs). Using analytical methods from the theory of viscosity solutions, we establish criteria for viability and invariance in terms of the first order normal cone. We also investigate reachability of arbitrary open sets. The method is based on viscosity techniques and duality for some associated linearized problem. The theoretical results are applied to general On/Off systems, Cook’s model for haploinsufficiency, and a stochastic model for bacteriophage λ.

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15 - Proactive Measures To Prevent Opioid Addiction

Summary

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks

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15 - Proactive Measures To Prevent Opioid Addiction

Summary

Viability, invariance and reachability for controlled piecewise deterministic Markov processes associated to gene networks