import numpy as np
import matplotlib.pyplot as plt

x0 = 100                # initial prey population
y0 = 8                  # initial predator pop.
a = 0.0015
b = 0.0003
c = 0.006
d = 0.5
N = 10000               # number of time units (days)
time = range(N+1)
x = np.zeros(len(time))
y = np.zeros_like(x)

x[0] = x0
y[0] = y0

for n in time[1:]:
    x[n] = x[n-1] + a * x[n-1] - b * x[n-1] * y[n-1]
    y[n] = y[n-1] + d * b * x[n-1] * y[n-1] - c * y[n-1]

plt.plot(time, x,label = 'Prey')
plt.plot(time, y, label = 'Predator')
plt.xlabel('Time')
plt.ylabel('Population')
plt.legend()
plt.show()