Modelling Miraa Addiction like a Disease Incorporating Voluntary Quitting

Abstract

This study presented a deterministic model of miraa addiction based on three compartmental classes incorporating miraa specific attributes as well as the aspect of voluntary quitting. Our model was based on SIS classical infectious model classes with Susceptible(S) and Infected (I) adopted as Light user (L) and Addicted (A) in our model. From the model flow chart, non linear differential equations are deduced. The basic reproduction number (R0) was determined using next generation method. Positivity and boundedness of the solution was investigated and the system of equations was found to lie in the feasible region. Miraa equilibrium points were determined and the condition necessary for the existence of miraa persistent equilibrium point was found to be R0 >1.  The conditions necessary for both local and global asymptotic stability of equilibrium points were determined. Sensitivity analysis of the  R0 was investigated using partial differentiation and then confirmed using normalized sensitivity analysis. Simulations were carried out using MATLAB ODE 45 inbuilt solver. Sensitivity analysis results revealed that the  R0 was directly proportional to the rate of quitting from addict to light user but inversely proportional to the rate of quitting from light user to susceptible. Therefore the rate of individuals moving from light user class to susceptible classes has higher impact on reducing the burden of miraa addiction than the rate of individuals moving from addict to light user. This study used theoretical data and parameters, future studies should consider fitting model to real data. The findings of this study will provide the stake holders including the government, NACADA, rehabilitation centres and general public with information of the spread of the addiction so that necessary measures may be taken to address the challenges. The model can find application in predicting future trends which is necessary for planning.  Control strategies can be instituted with the help of the model.