Pigs

$$ \begin{aligned} \frac{dS_p}{dt} &= b_p + \varepsilon_1 V_p - \Big[ \frac{\beta_P I_p}{N_p} + \frac{\beta_{WP} I_w}{N_w} + \frac{\beta_1 (S_1+F) I_p}{N_p} \Big](1-\mu_1)S_p f(\cdot) - \phi_1 S_p - \mu_p S_p \\ \frac{dE_p}{dt} &= \Big[ \frac{\beta_P I_p}{N_p} + \frac{\beta_{WP} I_w}{N_w} + \frac{\beta_1 (S_1+F) I_p}{N_p} \Big](1-\mu_1)S_p f(\cdot) - (\sigma_1+\mu_p)E_p \\ \frac{dI_p}{dt} &= \sigma_1 E_p - (\gamma_1 + C + d_1)I_p \\ \frac{dR_p}{dt} &= \gamma_1 I_p - \mu_p R_p + \theta_1 V_p \\ \frac{dV_p}{dt} &= \phi_1 S_p - (\varepsilon_1+\theta_1+\mu_p)V_p \end{aligned} $$

Wild Boar

$$ \begin{aligned} \frac{dS_w}{dt} &= b_w - \frac{\beta_{PW} I_p}{N_p}(1-\pi)S_w f(\cdot) - \mu_w S_w - \pi S_w \\ \frac{dI_w}{dt} &= \frac{\beta_{PW} I_p}{N_p}(1-\pi)S_w f(\cdot) - (\gamma_2 + d_2 + \mu_w)I_w \\ \frac{dR_w}{dt} &= \gamma_2 I_w + \pi S_w - \mu_w R_w \end{aligned} $$