Mathematical modeling, analysis, and optimal control of the n+7 compartment smoking epidemic model

Abstract

In this study, we present a new mathematical model for the n+7 compartment smoking epidemic and analyze its behavior using optimal control techniques. We examine the system’s basic properties and use Lyapunov functions and Routh-Hurwitz criteria to perform stability analysis. Our results show that the system is globally and locally asymptotically stable at the free equilibrium E₀ when R₀<1, and globally and locally asymptotically stable at the endemic equilibrium E^∗ when R₀>1. We also conduct a sensitivity analysis to identify the model parameters that significantly impact the reproduction number R₀. Our goal is to identify optimal strategies for minimizing the number of heavy smokers, maximizing the number of sick heavy smokers who receive hospital treatment, and increasing the number of rich and poor heavy smokers who seek treatment at private and public smoking treatment centers. We use Pontryagin’s maximum principle in continuous time to characterize the optimal controls, and we confirm our theoretical findings through numerical simulations conducted using Matlab.