$x=players\\ y=nonplayers\\ *->x ---k1\\ x->y ---k2\\ y->x ---k3\\ y->* ---k4$
k1=0.01
k2=10.0
k3=0.01
k4=0.01
k5=100.01
xl=[]
yl=[]
dt=0.0001
tf=10.0
tprt=0.1
xo=50000
yo=0.0
xn=xo
yn=yo
xl.append(xn)
yl.append(yn)
t=0.0
while t<tf:
#print t
xno=xn
yno=yn
xn+=dt*(k1+k3*yno-k2*xno)
yn+=dt*(k2*xno-k4*yno-k5)
if(t>tprt):
xl.append(xn)
yl.append(yn)
tprt+=0.1
#print t
if yn<0.0:
print("bye!")
break
t+=dt
#print t
#raw_input()
print("DONE")
DONE
#import matplotlib.pyplot as plt
#plt.plot(xl,"*")
#plt.plot(yl,"-")
#print xn
import math as mth
import random
No=5000
lmda=0.8
t=[]
np={}
t=range(1,360)
#print t
np[0]=No
delta=0
deltb=0
trelease=[10,50,75,100,150]
for i in t:
if i in trelease:
delta = random.randint(10000, 50000)*1/i
deltb = random.randint(2000, 5000)*1/i
print delta, deltb
else:
delta=0
deltb=0
#np[i]=-mth.log(i)+lmda*np[i-1]+delta
#np[i]=(0.00000000001/(i+1.0))+lmda*np[i-1]+delta
#np[i]=(1/(i+1))+lmda*np[i-1]+delta
#qx=50+random.randint(-20,20)
qx=random.randint(0,20)
#np[i]=qx+lmda*np[i-1]+delta
#new = math.exp(-i)*np[i-1]+delta
new = 0.25*np[i-1]+delta
rep = 1/i*np[i-1]+deltb
np[i]=new+rep
#print new, rep
#print np[i-1], np[i]
#print i
#print np
2071 332 230 67 611 50 438 33 175 28
import matplotlib.pyplot as plt
plt.plot(np.keys(),np.values())
plt.yscale('log')
#plt.xscale('log')
#plt.plot(yl,"-")