Usman Pagalay, Dewi Zumrotul Nafisa, Heni Widayani
Innate immune response in pneumonia on lung-macrophages patient can be modeled as a system of first order nonlinear differential equations. This model consists population of bacterial streptococcus pneumoniae, population of inactive macrophages, and population of active macrophages. We performed optimal control using Pontryagin Minimum Principle and using combination of finite difference and Runge Kutta 4th order in the simulation. The results show the difference of bacterial growth using control or not. This growth is suppressed by pro-inflammatory cytokines. If an individual has a good immune system then growth time of bacteria streptococcus pneumoniae becomes slower. Further, if an individual has a bad immune system, then growth time becomes faster. © 2019 Author(s).
Department of Mathematics, Maulana Malik Ibrahim Malang Islamic State University of Malang, Indonesia
