Sensitivity and mathematical model analysis on smoking with health education effect

Abstract

In this article we are given a mathematical model of smoking with health education effect. The solution of the model is positive (if the initial population is positive) and bounded. The reproductive number R0 is calculated from the model, and we show if R₀>1 the endemic equilibrium point exists and is unique, and if R₀≤1 the endemic equilibrium point does not exist. Smoking free equilibrium point is stable when R₀<1, and endemic equilibrium point is stable when R₀>1. Numerical simulation has been included to show stability and instability of equilibrium points. Furthermore, we study the relative change in R₀ if the value of the parameter changes, this is called sensitivity analysis of parameters involving in the reproductive number.