Analisis Dinamik Model Respon Inflamasi Pada Paru-Paru - Arrofiqi, Muhammad Rosyid; Pagalay, Usman; Nasichuddin, Achmad (Mathematics Department, Maulana Malik Ibrahim State Islamic University of Malang, 2023)
This study discusses the dynamic analysis of the inflammatory response model in the lungs. Then proceed with performing numerical simulations. This study was conducted to present the inflammatory response in the lungs. In the mathematical model of the inflammatory response, there are three variables, namely (pathogen), (immune system) and (inflammation). Dynamic analysis is carried out by determining the equilibrium point, the basic reproduction number , stability analysis of the equilibrium point. The results of this study obtained a basic reproduction number . The disease-free equilibrium point is unstable and the endemic equilibrium point is unstable when the parameter values in table 4.1 are used. The results of numerical simulations show that the population of pathogens found in the body starts from the first day, which is 0.01, increases to 2.8 until the second week, decreasing constantly accompanied by the immune system in the human body so that it goes to 0 at infinity. While the immune defense population in the human body rises to 4.4 and decreases slowly and constantly following the development of pathogens in the human body accompanied by the immune system itself. And the pro-inflammatory inflammation population runs steadily at 0 to rises at 4.3 following human immune defense and falls at week 16 and continues to be consistent. The rate of inflammation follows a hyperbolic tan which is affected by when t is infinite towards . When the parameter values and are increased, the pro-inflammatory inflammation will decrease and vice versa.