Relapse Processes are Important in Modelling Drug Epidemic
Alexander Yu Tang and Maurice HT Ling*
School of Applied Sciences, Temasek Polytechnic, Singapore
*Corresponding Author: Maurice HT Ling, School of Applied Sciences, Temasek Polytechnic, Singapore.
April 27, 2022; Published: May 12, 2022
Global drug epidemic is an important public health issue. Mathematical modelling is vital for gaining insights, which may inform policymaking. Several modelling studies fail to adequately address relapse, which includes rapid relapse into heavy or light drug use, and relapse after extended sobriety. Here, we study the impact of relapses by incorporating relapse processes into an existing 6-compartment model. Our results show that the proportions of drug users are higher with relapse processes than that without relapse processes; yet, the proportion of rehabilitation is lower with relapse than without relapse. This highlights the importance of relapse processes in modelling drug epidemic.
Keywords: Drug Epidemic Model; Relapse; ODE; Sensitivity Analysis
- Hedegaard H., et al. “Drug Overdose Deaths in the United States, 1999-2020”. NCHS Data Brief. (US Department of Health and Human Services), No. 428 (2021).
- Wang C., et al. “The Evolving Regulatory Landscape for Fentanyl: China, India, and Global Drug Governance. International Journal of Environmental Research and Public Health4 (2022): 2074.
- Das P and Horton R. “The Global Drug Problem: Change But Not Progression”. The Lancet10208 (2019): 1488-1490.
- Zaami S., et al. “New Trends of Substance Abuse During COVID-19 Pandemic: An International Perspective”. Frontiers in Psychiatry 11 (2020): 700.
- Imtiaz S., et al. “The Impact of the Novel Coronavirus Disease (COVID-19) Pandemic on Drug Overdose-Related Deaths in the United States and Canada: A systematic Review of Observational Studies and Analysis of Public Health Surveillance Data”. Substance Abuse Treatment, Prevention, and Policy1 (2021): 87.
- Ali F., et al. “Changes in Substance Supply and Use Characteristics Among People Who Use Drugs (PWUD) During the COVID-19 Global Pandemic: A National Qualitative Assessment in Canada”. International Journal of Drug Policy 93 (2021): 103237.
- Seltzer N. “The Economic Underpinnings of the Drug Epidemic”. SSM - Population Health 12 (2020): 100679.
- Mackintosh DR and Stewart GT. “A Mathematical Model of a Heroin Epidemic: Implications for Control Policies”. Journal of Epidemiology and Community Health4 (1979): 299-304.
- Wang W., et al. “A Scoping Review of Drug Epidemic Models”. International Journal of Environmental Research and Public Health4 (2022): 2017.
- Tang H., et al. “Modeling the Dynamics of Drug Spreading in China”. International Journal of Environmental Research and Public Health1 (2021): E288.
- Mousali AA., et al. “Factors Affecting Substance Use Relapse Among Iranian Addicts. Journal of Education and Health Promotion 10 (2021): 129.
- Njagarah JBH and Nyabadza F. “Modelling the Role of Drug Barons on the Prevalence of Drug Epidemics”. Mathematical Biosciences and Engineering3 (2013): 843-860.
- Dormand JR and Prince PJ. “A Family of Embedded Runge-Kutta Formulae”. Journal of Computational and Applied Mathematics1 (1980): 19-26.
- Ling MH. “COPADS IV: Fixed Time-Step ODE Solvers for a System of Equations Implemented as a Set of Python Functions”. Advances in Computer Science: an International Journal3 (2016): 5-11.
- Abou-Taleb KA and Galal GF. “A Comparative Study Between One-Factor-At-A-Time and Minimum Runs Resolution-IV Methods for Enhancing the Production of Polysaccharide by Stenotrophomonas daejeonensis and Pseudomonas geniculate”. Annals of Agricultural Sciences2 (2018): 173-180.
- Ling MH. “AdvanceSyn Toolkit: An Open Source Suite for Model Development and Analysis in Biological Engineering”. MOJ Proteomics and Bioinformatics4 (2020): 83-86.
- Willmott C and Matsuura K. “Advantages of the Mean Absolute Error (MAE) Over the Root Mean Square Error (RMSE) in Assessing Average Model Performance”. Climate Research 30 (2005): 79-82.
- Xia Y., et al. “Family Function Impacts Relapse Tendency in Substance Use Disorder: Mediated Through Self-Esteem and Resilience”. Frontiers in Psychiatry 13:815118.
- Ghitza UE. “Needed Relapse-Prevention Research on Novel Framework (ASPIRE Model) for Substance Use Disorders Treatment”. Frontiers in Psychiatry 6 (2015): 37.
- Rady A., et al. “Polysomnographic Correlates for the Risk of Relapse in Detoxified Opiate-Misuse Patients. Neuropsychiatric Disease and Treatment 16 (2020): 3187-3196.
- Dolsen MR and Harvey AG. “Life-Time History of Insomnia and Hypersomnia Symptoms as Correlates of Alcohol, Cocaine and Heroin Use and Relapse Among Adults Seeking Substance Use Treatment in the United States from 1991 to 1994”. Addiction6 (2017): 1104-1111.
- Plaza-Zabala A., et al. “The Hypocretin/Orexin System: Implications for Drug Reward and Relapse. Molecular Neurobiology3 (2012): 424-439.
- Lachowicz M., et al. “Significant Association of DRD2 and ANKK1 Genes with Rural Heroin Dependence and Relapse in Men. Annals of Agricultural and Environmental Medicine2 (2020): 269-273.
- Hudson A and Stamp JA. “Ovarian Hormones and Propensity to Drug Relapse: A Review”. Neuroscience and Biobehavioral Reviews3 (2011): 427-436.
- Mussulman LM., et al. “Rapid Relapse to Smoking Following Hospital Discharge”. Preventive Medicine Reports 15 (2019): 100891.
- Cornelius JR., et al. “Rapid Relapse Generally Follows Treatment for Substance Use Disorders Among Adolescents”. Addictive Behaviors2 (2003): 381-386.
- Ramo DE., et al. “Variation in Substance Use Relapse Episodes Among Adolescents: A Longitudinal Investigation”. Journal of Substance Abuse Treatment1 (2012): 44-52.
- Hickman M., et al. “Estimating the Prevalence of Problematic Drug Use: A Review of Methods and Their Application”. Bulletin on Narcotics1-2 (2002): 15-32.
- Zhao Y. “Estimating the Size of an Injecting Drug User Population”. World Journal of AIDS03 (2011): 88-93.
- Wu J., et al. “Using Data from Respondent-Driven Sampling Studies to Estimate the Number of People Who Inject Drugs: Application to the Kohtla-Järve Region of Estonia”. PLoS ONE11 (2017): e0185711.
- Wejnert C., et al. “Estimating Design Effect and Calculating Sample Size for Respondent-Driven Sampling Studies of Injection Drug Users in the United States”. AIDS and Behavior4 (2012): 797-806.
- Xu Y., et al. “Estimating the Number of Injection Drug Users in Greater Victoria, Canada Using Capture-Recapture Methods”. Harm Reduction Journal1 (2014): 9.
- Allen ST., et al. “Estimating the Number of People Who Inject Drugs in A Rural County in Appalachia”. American Journal of Public Health3 (2019): 445-450.
- Zhang G., et al. “Estimating Prevalence of Illicit Drug Use in Yunnan, China, 2011-15. Frontiers in Psychiatry 9 (2018): 256.
- Jalali MS., et al. “Data Needs in Opioid Systems Modeling: Challenges and Future Directions. American Journal of Preventive Medicine2 (2021): e95-e105.
- Sharareh N., et al. “Evidence of Modeling Impact in Development of Policies for Controlling the Opioid Epidemic and Improving Public Health: A Scoping Review”. Substance Abuse: Research and Treatment 13 (2019): 1178221819866211.