Study on Opioids Diffusion Based on Improved SIR Model

Source:
By:YaNing Tan, JiaQi Wu, Zeming Jin

DOI: https://doi.org/10.30564/jams.v3i2.1720

Abstract:

The abuse of opioids is harmful to the national economy and health. The U.S. government has spent a lot of time, energy and money to deal with this phenomenon. Based on the topic background and team discussion, we deeply excavated the data and information provided in the topic, determined the current use of opioids, and constructed an improved SIR model to determine the source of drug abuse, the mechanism of drug abuse diffusion and the origin of each state through reverse derivation, which provided guidance for the government in the context of opioid abuse.Based on the above results, we simulated and analyzed the improved SIR model and determined the accuracy and stability of the model in the data set.

References:

[1]Florence C S , Zhou C , Luo F , et al. The Economic Burden of Prescription Opioid Overdose, Abuse, and Dependence in the United States, 2013[J]. Medical Care, 2016, 54(10):901-906. [2]Yang J , Liang S , Zhang Y . Travelling Waves of a Delayed SIR Epidemic Model with Nonlinear Incidence Rate and Spatial Diffusion[J]. Plos One, 2013, 8(8):e21128. [3]Towers S ,Geisse K V , Zheng Y , et al. Antiviral treatment for pandemic influenza: Assessing potential repercussions using a seasonally forced SIR model[J]. Journal of Theoretical Biology, 2011, 289(none):259-268. [4]Inaba H . Mathematical analysis of an age-structured SIR epidemic model with vertical transmission[J]. Discrete and Continuous Dynamical Systems - Series B (DCDS-B), 2017, 6(1):69-96. [5]Xu J , Xu Y . Grey correlation-hierarchical analysis for metro-caused settlement[J]. Environmental Earth Sciences, 2011, 64(5):1249-1256.