{ diff(x1, t) = (1*k12*(k1 + k2*x1*(1 - (x1 + 1)/k3)) + (-1)*k12*(k4*x1 + (1 - k10*k11)*k5*x3*x1))/k12,
  diff(x2, t) = (1*k12*(1 - k10*k11)*k5*x3*x1 + (-1)*k12*k6*x2)/k12,
  diff(x3, t) = (1*k12*(1 - (k9 + k11)/2)*k7*x2 + (-1)*k12*k8*x3)/k12,
  diff(x4, t) = (1*k12*(k9 + k11)/2*k7*x2 + (-1)*k12*k8*x4)/k12 }