Model Mathematics

P = P_1 + P_2 H = S + I_1 + R_1 + I_2 + R_2 + I_12 + I_21 + R_12 \frac{d}{d time} (S) = (\frac{r H}{epsilon H + 1} - (d S) - (beta_1 S P_1) - (beta_2 S P_2)) + g (R_1 + R_2 + R_12)

\frac{d}{d time} (I_1) = beta_1 S P_1 - (a_1 I_1) - (alpha_1 I_1)

\frac{d}{d time} (I_2) = beta_2 S P_2 - (a_2 I_2) - (alpha_2 I_2)

\frac{d}{d time} (I_12) = beta_2 R_1 P_2 - (a_2 I_12) - (alpha_2 I_12)

\frac{d}{d time} (I_21) = beta_1 R_2 P_1 - (a_1 I_21) - (alpha_1 I_21)

\frac{d}{d time} (R_1) = alpha_1 I_1 - (d R_1) - (g R_1) - (beta_2 R_1 P_2)

\frac{d}{d time} (R_2) = alpha_2 I_2 - (d R_2) - (g R_2) - (beta_1 R_2 P_1)

\frac{d}{d time} (R_12) = alpha_2 I_12 + alpha_1 I_21 - (d R_12) - (g R_12)

\frac{d}{d time} (P_1) = k_1 (I_1 + I_21) - (u P_1) log_P1 = \log_{10} P_1

\frac{d}{d time} (P_2) = k_2 (I_2 + I_12) - (u P_2) log_P2 = \log_{10} P_2

G = \frac{1}{g}