Study of Opioid Crisis with SI Model Based on Data

With the number of opioid overdose fatalities steadily increasing since the 1990s, opioid addiction has become a global epidemic and a national health crisis in recent years. The abuse of opioids has profoundly affected all aspects of the social economy. Therefore, it is particularly important to model the transmission trend of opioid abusing and to predict the distribution of opioid abusing between different regions. Our work is inspired by the Mathematical Contest in Modelling (MCM) 2019. In this paper, an ODE model is established to analyze the dynamics of opioid addiction. Meanwhile, the stability of the model is also analyzed. In the fourth part of this paper, we select the data from 2010 to 2016 of a particular county for analysis. Comparing the fitting results with the actual data, the fitting results is acceptable and then we use the model to forecast the data for the next two years.

[1]  A. Ferrari,et al.  Global statistics on alcohol, tobacco and illicit drug use: 2017 status report , 2018, Addiction.

[2]  L. Paulozzi.  Prescription drug overdoses: a review. , 2012, Journal of safety research.

[3]  Qiuhui Pan,et al.  Population Dynamics of Patients with Bacterial Resistance in Hospital Environment , 2016, Comput. Math. Methods Medicine.

[4]  P. Skolnick,et al.  Annual Review of Pharmacology and Toxicology The Opioid Epidemic : Crisis and Solutions , 2017 .

[5]  Tailei Zhang,et al.  Global behaviour of a heroin epidemic model with distributed delays , 2011, Appl. Math. Lett..

[6]  Greg Freedman,et al.  Global burden of disease attributable to illicit drug use and dependence: findings from the Global Burden of Disease Study 2010 , 2013, The Lancet.

[7]  J. Watmough,et al.  Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. , 2002, Mathematical biosciences.

[8]  E. White,et al.  Heroin epidemics, treatment and ODE modelling. , 2007, Mathematical biosciences.

[9]  J. Glanz,et al.  National trends in pharmaceutical opioid related overdose deaths compared to other substance related overdose deaths: 1999-2009. , 2013, Drug and alcohol dependence.

[10]  Nicholas A. Battista,et al.  Modeling the Prescription Opioid Epidemic , 2017, Bulletin of Mathematical Biology.

[11]  Michael Y. Li,et al.  Global dynamics of a discrete age-structured SIR epidemic model with applications to measles vaccination strategies. , 2019, Mathematical biosciences.

[12]  L. Nummenmaa,et al.  Opioid system and human emotions , 2018, British journal of pharmacology.

[13]  Jill Barr-Walker,et al.  Fentanyl, fentanyl analogs and novel synthetic opioids: A comprehensive review , 2017, Neuropharmacology.

[14]  Carlos Castillo-Chavez,et al.  On the Computation of R(o) and Its Role on Global Stability , 2001 .

[15]  Christopher M. Jones,et al.  Vital Signs: Demographic and Substance Use Trends Among Heroin Users — United States, 2002–2013 , 2015, MMWR. Morbidity and mortality weekly report.

[16]  Philippe Bourgois,et al.  "Every 'never' I ever said came true": transitions from opioid pills to heroin injecting. , 2014, The International journal on drug policy.