Table 1 Model parameters and their descriptions.
From: Mathematical modeling and analysis of the co-dynamics of crime and drug abuse
Symbol | Intepretation | Range/value | Source |
|---|---|---|---|
\(\Lambda\) | Recruitment rate | [0.001, 0.1] | Assumed |
\(\beta _c\) | Crime diffusion rate | 0.0505 | |
\(\beta _a\) | Substance abuse diffusion rate | 0.0427 | |
\(\omega\) | The modification parameter | [0, 1] | Assumed |
\(\sigma _c\) | Rate of progression to criminal behavior | 1/100 | Assumed |
\(\sigma _a\) | Rate of progression to substance abuse behavior | 0.024 | |
\(\sigma _e\) | Rate of developing co-occurring behaviors | [1/14, 1/3] | Assumed |
\(\theta _{c}\) | Incarceration rate | [0.00016, 0.006] | |
\(\theta _a\) | Substance abused rehabilitation rate | [0.11, 0.13] | |
\(\theta _e\) | Co-engaged rehabilitation rate | [0.00016, 0.13] | |
\(\kappa _{c}\) | Recidivism rate of criminals | [0.1, 0.63] | |
\(\kappa _a\) | Relapse rate after rehabilitation | [0.4, 0.6] | |
\(\kappa _e\) | Co-occurring recidivism rate | [0.1, 0.63] | |
\(\phi _c\) | Rehabilitated crime individuals recovery rate | [0.37, 0.9] | |
\(\phi _a\) | Substance rehab recovery rate | [0.4,0.89] | |
\(\phi _e\) | Rehabilitated co-engaged individuals recovery rate | [0.1, 0.63] | |
\(\gamma _{c}\) | Recovery rate of criminal individuals | [0.37, 0.9] | |
\(\gamma _a\) | Recovery rate of substance -abuse individuals | [1/90, 1/7] | |
\(\gamma _e\) | Recovery rate of co-engaged individuals | [0.37, 0.9] | |
\(\tau _{c}\) | Crime resilience rate | [0, 1] | Assumed |
\(\tau _a\) | Substance abuse resilience rate | [0, 1] | Assumed |
\(\delta _{c}\) | Death rate due to crime | [0.001, 0.1] | |
\(\delta _a\) | Death rate due to substance abuse | [0.001, 0.1] | |
\(\delta _e\) | Death rate due to co-occurring | [0.001, 0.1] | Assumed |
\(\mu\) | Natural death rate | [0.001, 0.1] | Assumed |
