nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

42 The DuCa Model
Figure 5.12 shows simulations of the irreducible model made with matlab where k = 0, f1 =
1.29 × 10 −5 ml cell −1 d −1 , f2 = 5.66 × 10 −5 ml cell −1 d −1 , and the term −cMa has been added in
equation 5.7 to model turnover of active macrophages. The initial values are that of a healthy
rest state. On the left we have the log-concentration versus time plots of the concentrations.
On the right is a phase space plot of M versus Ma.
Figure 5.13 shows a simulation made
with matlab of the reversible model
where a term of −cMa has been added to
equation 5.7 to model turnover of active
macrophages. The simulation is done
with f1 = 1.31 × 10 −5 ml cell −1 d −1 , f2 =
5.18 × 10 −5 ml cell −1 d −1 and initial
conditions that simulate a healthy rest
state.
fails to exhibit Balb/c dynamics as observed in experiments. In figure 5.14 we see the
solution curves of the respective concentrations in a log-concentration versus time plot,
and a phase space portrait of the resting versus active macrophages. The phase space
portrait shows that a so-called limit cycle exists for (f1, f2) = (1.88, 5) in the DuCa
model with Ma-efflux.