I'm getting an 'index out of bounds' error using solve_ivp

Question

I'm trying to find the outbreak time (when the number of zombies >= number of humans) as a function of the zombification rate gamma, using the following code:

arrOutbreakT = []
arrGamma = np.linspace(10**(-4), 1, 2001)

for i in range (0, len(arrGamma)):
    gamma = arrGamma[i]
    NstepC = (gamma*10000).astype(int)
    tlistC = np.linspace(iniTime, finalTime, NstepC + 1)
    solC = solve_ivp(gradF, t_span2, ini2, t_eval = tlistC)
    
    k = 0
    klist = np.zeros(NstepC+1)
    while solC.y[1, k] < (solC.y[0, k] / 4):
        k = k + 1
        
    arrOutbreakT.append(tlistC[k])

where

alpha = 0.0 # human natural birth rate
beta = 1.0*(10**(-4)) # human natural death rate
gamma = 9.5*(10**(-3)) # zombification rate
delta = 1.0*(10**(-4)) # zombie destruction rate
epsilon = 1.0*(10**(-4))
iniTime = 0.0
h = 0.01 # step size
Nstep = 500
finalTime = iniTime + Nstep*h # = 5.0 days

H0 = 1000 # original no. of humans
Z0 = 5 # original no. of zombies
D0 = 0 # original no. of dead

ini2 = [H0, Z0, D0]
t_span2 = [time[0], finalTime]

def gradF (time, HZD):
    return [(alpha - beta - gamma*HZD[1])*HZD[0], 
            gamma*HZD[0]*HZD[1] - delta*HZD[0]*HZD[1] + epsilon/HZD[1], 
            beta*HZD[0] + delta*HZD[0]*HZD[1] - epsilon*HZD[2]]

I get this output:

IndexError                                Traceback (most recent call last)
    321 k = 0
    322 klist = np.zeros(NstepC+1)
--> 323 while solC.y[1, k] < (solC.y[0, k] / 4):
    324     k = k + 1
    326 arrOutbreakT.append(tlistC[k])

IndexError: index 2 is out of bounds for axis 1 with size 2

Can someone help?

where is 'time' defined for 'time[0]'?

chitown88
– chitown88

2025-11-12 16:48:27 +00:00
Commented Nov 12 at 16:48 — chitown88
– chitown88, Commented Nov 12 at 16:48

louis thomas · Accepted Answer · 2025-11-12 16:39:11Z

3

You’re running past the end of your solution array — your while loop keeps incrementing k until it exceeds the last index of solC.y.

Use a bounded loop condition instead, e.g.:

k = 0
while k < solC.y.shape[1] and solC.y[1, k] < solC.y[0, k] / 4:
    k += 1

if k == solC.y.shape[1]:
    # outbreak never reached; handle accordingly
    arrOutbreakT.append(np.nan)
else:
    arrOutbreakT.append(tlistC[k])

The IndexError happens because your condition is never met before k exceeds solC.y.shape[1]-1.
Always check k < solC.y.shape[1] in loops like this.

answered Nov 12 at 16:39

louis thomas

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chitown88 · Accepted Answer · 2025-11-12 16:56:34Z

0

gradF function outputs an array of 3 elements. solC as you see is an array of 3 elements (see below). After the 3rd loop, and solC.y[1, k] < (solC.y[0, k] / 4) is still True, it goes into k=3 for the 4th loop, but there is no 4th element.

array([[1000.        ,  997.00447058],
      [   5.        ,    5.0001    ],
      [   0.        ,    2.99478029]])

answered Nov 12 at 16:56

chitown88

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