Fig. 5
From: Reducing M2 macrophage in lung fibrosis by controlling anti-M1 agent
Dynamical system for M2 density with different constant scalar values for \(\eta _{M1}(t)\). The dynamical system (2) for M2 at point p, located at the center of square D, is solved using the Lagrangian spectral method for N=32, with different \(\eta _{M1}(t)\) values, for fibrosis scars in lung tissue (see section “Legendre spectral method in two-dimensions”). For \(\eta _{M1}(t)=0\) we have Case I, while for Case II different valuse of \(\eta _{M1}(t)= 0.4 \times 10^{-3}, 0.4 \times 10^{-2}, 0.1 \times 10^{-1}\), and \(0.4 \times 10^{-1}\) are considered. It is clear that the closer \(\eta _{M1}(t)\) gets to zero, the higher M2 density becomes. This figure uses different colors to show the decreasing levels of M2 density for various increasing values of \(\eta _{M1}(t)\) ( \(\eta _{M1}(t) \in [0, 0.4\times 10^{-1} ]\)). These graphs demonstrate that as \(\eta _{M1}(t)\) decreases over time, M2 density increases, however, the graphs of M2 density over time continue to trend upward.
