Abstract
Tramadol initially use as an analgesic which lead to addiction and overdose worldwide due to prolong consumption, particularly in low and middle income countries. This paper deals with a mathematical approach of Multiple Relapse Tramadol Abuse Model (MRTAM) to analyze affected population with time domain. This model is a non-linear compartmental framework, which simulates the abuse progression. Parameters such as prevention rate (σ), relapse rate (ξ2), treatment rate (ξ1), and law enforcement (η) influence the abuse population and the reproduction number (R0). Eigenvalues of the dynamics are derived to analyze the stability and behavior of the system. Results show that the system is highly sensitive to prescription inflow, progression and prevention parameters. Endemic equilibrium is obtained and also presented the analysis of bifurcation and partial rank correlation coefficient (PRCC) to quantify and assess the influence of various parameters on the abuse population.
MSC Classification: 92C60; 92D25
