Model Mathematics

\frac{d}{d time} (S) = rs S ((1 - (u 1)) + \frac{beta epsilon_s u}{1}) + \frac{alpha u rs S}{1} (1 - epsilon_s) - (phi S 1)

\frac{d}{d time} (M) = rm M ((1 - (\frac{u}{1})) + \frac{beta epsilon_m u}{1}) + \frac{alpha u rm M}{1} (1 - epsilon_m) - (phi M 1)

phi = \frac{S rs}{1} (1 - (\frac{u}{1} (1 - (\frac{beta epsilon_s}{1}) - (\frac{alpha}{1} (1 - (\frac{epsilon_s}{1})))))) + \frac{M rm}{1} (1 - (\frac{u}{1} (1 - (\frac{beta epsilon_m}{1}) - (\frac{alpha}{1} (1 - (\frac{epsilon_m}{1})))))) growth_rate = (rs + rm) (1 - (\frac{a}{1}))