# Model of cancer and the immune system (Nelson, Naini and Nagy 2003).  Assumes the tumor is a sphere and 
# the immune system can only attack a rind around the edge.  So there are no real TIL.  The depth to which
# immune effector cells can penetrate is measured by parameter beta (be).  We also assume that the only cancer
# cells capable of reproduction are along the outside rind.
#
#  Variables:
#     L : Mass of immune effector cells (=Lymphocytes, mg)
#     C : Mass of cancer cells (g)
#
#  Parameters:
#     al1  : Intrinsic reproductive rate of lymphocytes
#     al2  : Intrinsic reproductive rate of cancer cells
#     be   : Depth of rind around the tumor containing reproductively active and immune-susceptable cells
#     K    : Maximum number of lymphocytes the body can maintain
#     Lam1 : Mortality rate of lymphocytes
#     Lam2 : Base rate at which lymphocytes kill cancer cells
#------------------------------------------------------------------------------------------------------------
# Vector field:
C'=al2*be*C^(2/3)-lam2*L*(C-be*C^(2/3))
L'=al1*(C-be*C^(2/3))*L*(1-(L/K))-lam1*L
#-------------------------------------------------------------------------------------------------------------
# Parameters:
p al1=0.0185, al2=1.4, lam1=0.7, lam2=0.085, be=0.2, K=50
#-------------------------------------------------------------------------------------------------------------
# Initial conditions: 
I L=0.1,C=1
#-------------------------------------------------------------------------------------------------------------
# Control stuff
@ bounds=100000, total=200, delay=10, Xlo=0, Xhi=200, Ylo=0, Yhi=140, MaxStore=1000000
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