Note: This is only a quick preview of our report. For more detail, if you are interested in this work, please contact waynemaibutterfly@gmail.com for the full report.

Introduction

Background

It is a serious problem that the abuse of synthetic and non-synthetic opioid have become a crisis to the public health and economic development.Further,health cost and assisted living facility staffing will also be affected by the the increasing percentage of people with opioid addiction within the elderly.The DEA/National Forensic Laboratory Information System(NFLIS) published a data-heavy annual report addressing on drug identification results and associated information from drug cases analyzed by federal,state,and local forensic laboratories,which handled over 88% of the nation's estimated 1.2 million annual state and local drug cases. Focusing on five states:Ohio,Kentucky,West Virginia,Virginia,and Tennessee, we need to analyse the trends of population on opioid using and identify a possible strategy for countering the opioid crisis.

Restatement of the Problems

For part one: We are required to build a mathematical model to describe the spread and characteristics of the reported synthetic opioid and heroin incidents in and between the five states and their counties over time.For the counties where had not found the specific opioid use,we can predict their developing trends and identify the possibility on the beginning of opioid abuse,as well as when and where the drug identification threshold levels occur.

For part two:We are required to modify our model to analyse the reason for the overuse of opioid with concluding important factors on drug abusing from part one such as social circumstance, economic condition and so on.Besides, we need to find out which group of people overuse the drug which contribute to the increasing percentage of drugster.

For part three: Combining the results of part one and part two,we can identify a possible strategy for countering the opioid crisis. Tested by the model we built, we need to analyse the effectiveness of the strategy and the sensitivity of our model.

Assumption and Justification

• The total number of people in each county is the same. Each non-drug user has the same possibility to addict drug.

• The initial number of mild drug addict in each county of five states is 0.

• The mild drug people will have a high probability of taking drugs again.

• Compared to the rate that drug spread in the same county, the rate that drug spread among different county is one-tenth of that in the same county.

• The distance between the position of a person to the center position of his/her home county obey a normal distribution with a mean of 0 and a variance of $\sigma$ .