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Estimating Opioid Drug Overdoses with Mathematical Models

By Dan Connors

An epidemic of opioid drug overdoses is occurring in the United States. According to the Centers for Disease Control and Prevention (CDC), there has been a 137% increase in the number of drug overdoses and a 200% increase in the number of overdose deaths since 2000.  This epidemic is hitting both our rural areas and our major cities.  

An epidemic of opioid drug overdoses is happening in the U.S.
1. Analyze the trends in overdose deaths for a large state and a small state and develop models to estimate the number of deaths that will occur due to overdoses in 2020 for the these two states.

2. Where are these drugs coming from and how can these sources be controlled? The CDC lists four types of opiods:

i. Natural opioid analgesics, including morphine and codeine, and semi-synthetic opioid analgesics, including drugs such as oxycodone, hydrocodone, hydromorphone, and oxymorphone;

ii. Methadone, a synthetic opioid;

iii. Synthetic opioid analgesics other than methadone, including drugs such as tramadol and fentanyl; and

iv. Heroin, an illicit (illegally-made) opioid synthesized from morphine that can be a white or brown powder, or a black sticky substance.

3. These drugs can be obtained by legal and illegal prescriptions and by illegal synthesis.  Develop a model to determine for these three sources of opiods and the four opiod types, the percentage of each pair (source, type) that are contributing to the US opiod overdose crisis, i.e., create a 3x4 grid with the opiod sources being the rows and the opiod types being the columns.

4. The federal government and state and local governments are enacting new policies to curb the supply of opiods.  How effective will these be?  To answer this choose at least two different two different policies that have been enacted or proposed and re-compute the table you computed in (3) above to reflect the impact of these policies.

5. Naloxone is a drug administered to victims of opiod overdoses that temporarily blocks the effects of opiods.  It has been hailed as a miracle drug and a lifesaver for many overdose victims.  However, there are critics of this miracle drug suggesting that the availability of this lifesaver encourages some to take more chances with opiods. These critics point to examples of people who have been revived several times with naloxone. Is naloxone encouraging risky behavior?  

The post is republished from the Moody's Mega Math Challenge website.

Dan Connors is a Research Staff Member at IBM.

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