Open AccessStability Analysis and Optimal Control of Lung Cancer Growth Model with Education
Author(s) -
Trisilowati
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/546/5/052081
Subject(s) - equilibrium point , population , lung cancer , optimal control , mathematics , control theory (sociology) , extinction (optical mineralogy) , nonlinear system , stability (learning theory) , mathematical optimization , control (management) , medicine , differential equation , computer science , mathematical analysis , physics , oncology , environmental health , machine learning , quantum mechanics , artificial intelligence , optics
This study discusses the influence of smoking behavior of both active and passive smokers on the growth of lung cancer population through mathematical models. There are four population in this model, namely: susceptible population, active smoker population, passive smoker population, and population of lung cancer patients. The model is then analyzed using stability theory of nonlinear differential equations. Based on analysis result, the model has three equilibrium points: extinction equilibrium point, smoker-free equilibrium point and endemic equilibrium point. These equilibrium points are asymptotically stable under certain conditions. Moreover, education is involved as a control which is applied to susceptible population. The purpose of this optimal control is to minimize the population of smokers and lung cancer as well as the education costs. Pontryagin’s principle is then implemented to solve optimal control problems. Finally, numerical simulations are carried out to determine the effectiveness of the controls used.