\begin{subequations}
    \begin{eqnarray}
        \dot{s}=-\beta_{uu} is-\beta_{vu} ds-\zeta s,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{i}=\beta_{uu} is + \beta_{vu} ds -\xi_{i}i-\gamma_{i}i,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{d}=\beta_{vv}iv + \beta_{uv}dv-\xi_{d}d - \gamma_{d}d,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{a}=\xi_{i}i-\gamma_{\alpha}\alpha-\mu_{\alpha}\alpha,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{r}=\gamma_{i}i+\gamma_{d}d+\gamma_{\alpha}\alpha+\gamma_{h}h,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{e}=\mu_{\alpha}\alpha+\mu_{h}h,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{v}=\zeta s -\beta_{vv}iv-\beta_{uv}dv,
    \end{eqnarray}
    \begin{eqnarray}
        \dot{h}=\xi_{d}d-\gamma_{h}h-\mu_{h}h,
    \end{eqnarray}
    \begin{eqnarray}
s(0)=s_{0},i(0)=i_{0},d(0)=d_{0},\alpha(0)=\alpha_{0},\\r(0)=r_{0},e(0)=e_{0},v(0)=v_{0},h(0)=h_{0},\nonumber
    \end{eqnarray}
    \label{eq:dynamics}
\end{subequations}
