Population/water/food evolution model

Time has unit t
W is water (unit : w), F is food (unit : f), P is population (unit : p), br is birth rate (unit : p/t) and dr is death rate (unit : p/t)
kW is water consumption (unit : w/p/t) and kF is food consumption (unit : f/p/t)
alpha > 0

dW/dt = -kW * P
dF/dt = -kF * P
dP/dt = br - dr
br = P / 10 * (1 - exp(-W * (1 + F)))
dr = minDR + 1 / (1 - exp(-W * (1 + F))) - 1

Solve this numerically for P, W and F (ODE's won't work)