# 
# HIV Project for Calculus
#



#numerical parameters
@ MAXSTOR=5000000
@ BOUNDS=1e+30
@ DT=0.05
@ TOTAL=30
@ METHOD=stiff


# This bit of codes sets up the graphing components (i.e., bounds and which quantities we are plotting

@ xlo=0,xhi=30
@ ylo=-10,yhi=20
@ ylo=-1e5,yhi=1.2e6
@ axes=2,lt=6
# number of plots on a graph
@ nplot=2
#@ xp=t,yp=logx,yp2=logy,yp3=logv
@ xp=t,yp=x,yp2=y


# auxilary functions
aux logx=log(x)
aux logy=log(y)
aux logv=log(v)


# Setting parameters
param lambda=1e5
param d=0.1 
param a=0.5 
param beta=2e-7
param k=100 
param u=5



# Defining the dynamics
dx/dt=lambda-d*x-beta*x*v
dy/dt=beta*x*v-a*y
dv/dt=k*y-u*v

########################
### INITIAL CONDITIONS 
########################



# initial value has to be entered but should equal x_init=lambda/d

x(0)=1e6
y(0)=0
v(0)=1

END