Kumar, Kirthi

English

ISU ReD: Research and eData

Presentation for the Symposium on BEER October 2019Mathematical Modeling, Analysis, Simulation of theOpioid Crisis with Prescription and Social DrugAddiction ModelsKirthi Kumar1,*, Dr. Padmanabhan Seshaiyer2, Dr. Carmen Caiseda31 Thomas Jefferson High School for Science and Technology, Alexandria, VA2 Department of Mathematical Sciences, George Mason University, Fairfax, VA, USA 3 InterAmerican University ofPuerto Rico, Bayamon, PRkirthi.kumar50@gmail.comAccording to the Centers for Disease Control, opioid overdose rates are rising, and data suggests that bothprescription and illicit drugs are significant with respect to the opioid crisis. This is an international problemthat affects social and economic welfare as well as public health. The typical framework for mathematicalmodels involves the classic compartmental model involving ordinary differential equations (ODE) that de-scribe phases of infectious diseases. Mathematical modeling for drug addiction as an infectious disease modelcan be a novel and unique method of approaching this issue, in particular with the addition of technologicalrehabilitation as a viable method of drug rehabilitation. This project explores two mathematical models,including one describing the dynamics of addiction through over prescription, and the second describingthe dynamics of addiction influenced by social behavior with ODE. In addition, parameters are estimatedwith AMPL optimization and machine learning; a rural vs. urban prescription model is studied; a basicreproduction number for social model is derived; efforts to support healthcare providers and education asa control for the opioid crisis are also explored; a numerical simulation of each model is implemented withhigh-order numerical approximation; and a graphical user interface is developed through MATLAB. Wehope to validate the mathematical models with real data and incorporate intervention with rehabilitationtechnology to further enhance the models to be more predictive.

Mathematical Modeling, Analysis, Simulation of the Opioid Crisis with Prescription and Social Drug Addiction Models

https://ir.library.illinoisstate.edu/cgi/viewcontent.cgi?article=1383&context=beer

Mathematical Modeling, Analysis, Simulation of the Opioid Crisis with Prescription and Social Drug Addiction Models

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ISU ReD: Research and eData