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.