# Model of viral infection with many different cell types (Kelly et al. 2003; Am. Nat.)
# Initial parameters represent HIV infecting two cell types.
#
#  Variables:
#     HIV : number of free HIV virions
#     T4u : number of uninfected T4 cells
#     T4i : number of infected T4 cells
#     Macu : number of uninfected macrophages
#     Maci : number of infected macrophages
#     Memu : number of uninfected memory cells
#     Memi : number of infected memory cells
#
#  Parameters:
#     v  : Burst size (number of virions released per dying cell)
#  muiT4, muT4 : Mortality rate of infected, uninfected T4 cells
#  muiMa, muMa : Mortality rate of infected, uninfected macrophages
#  muiMe, muMe : Mortality rate of infected, uninfected memory T cells
#    muv : Clearance rate of free virions
#   beT4 : Infection constant for T4 cells
#   beMa : Infection constant for macrophages
#   beMe : Infection constant for memory cells
#  LamT4 : Input rate of uninfected T4 cells
#  LamMa : Input rate of uninfected macrophages
#  LamMe : Input rate of uninfected memory cells
#  
#  NOTE: in the HIV equation I'm assuming that burst size v is the same for all cell types, an assumption
#  that the authors do not make.
#------------------------------------------------------------------------------------------------------------
# Vector field:
HIV'  = v*(muiT4*T4i + muiMa*Maci + muiMe*Memi) - muv*HIV - HIV*(beT4*T4u + beMa*Macu + beMe*Memu)
T4u'  = lamT4 - muT4*T4u - beT4*T4u*HIV
T4i'  = beT4*T4u*HIV - muiT4*T4i
Macu' = lamMa - muMa*Macu - beMa*Macu*HIV
Maci' = beMa*Macu*HIV - muiMa*Maci
Memu' = lamMe - muMe*Memu - beMe*Memu*HIV
Memi' = beMe*Memu*HIV - muiMe*Memi
#-------------------------------------------------------------------------------------------------------------
# Parameters:
p v=900, muT4=0.1, muiT4=0.5, muMa=0.1, muiMa=0.3, muMe=0.1, muiMe=0.1, muv=4
p beT4=0.0001, beMa=0.00003, beMe=0.0001, LamT4=10, LamMa=2, LamMe=10
#-------------------------------------------------------------------------------------------------------------
# Initial conditions: 
I HIV=1, T4u=10, T4i=0, Macu=10, Maci=0, Memu=1, Memi=0
#-------------------------------------------------------------------------------------------------------------
# Control stuff
@ bounds=100000, total=100, delay=10, Xlo=0, Xhi=100, Ylo=0, Yhi=6000, MaxStore=1000000
d