Prova
`\begin{multline*}
\sum _{i=1} ^N \int\limits_0^{\overline t} \left\{ \left( –
\dfrac{\partial R_i (t,e^{\bullet i})}{\partial e^i}
+ \dfrac{\partial D_i (t,e^{\bullet} I^{\bullet})}{\partial e^i} \right) (e^i (t)
– e^{\bullet i} (t)) \right. \\
\shoveleft + \left( \dfrac{\partial C_i (t,I^{\bullet i})}{\partial I_i^i}
+ \dfrac{\partial D_i (t, e^{\bullet}, I^{\bullet})}{\partial I_i^i} \right) (I_i^i (t)
– I_i^{\bullet i} (t)) \\
\shoveleft + \left. \sum _{j=1}^N
\left( \dfrac{\partial C_i (t,I^{\bullet i})}{\partial I_j^i}
+ \dfrac{\partial D_i (t,e^{\bullet}, I^{\bullet})}{\partial I_j^i} \right)
(I_j^i (t) – I_j^{\bullet i} (t)) \right\} \, \text{d}t \geq 0 \\
\shoveleft {}\mkern5mu
\forall (e,I) \in K(e^\bullet, I^\bullet). \hfill
\end{multline*}`
\begin{multline*}
\sum _{i=1} ^N \int\limits_0^{\overline t} \left\{ \left( –
\dfrac{\partial R_i (t,e^{\bullet i})}{\partial e^i}
+ \dfrac{\partial D_i (t,e^{\bullet} I^{\bullet})}{\partial e^i} \right) (e^i (t)
– e^{\bullet i} (t)) \right. \\
\shoveleft + \left( \dfrac{\partial C_i (t,I^{\bullet i})}{\partial I_i^i}
+ \dfrac{\partial D_i (t, e^{\bullet}, I^{\bullet})}{\partial I_i^i} \right) (I_i^i (t)
– I_i^{\bullet i} (t)) \\
\shoveleft + \left. \sum _{j=1}^N
\left( \dfrac{\partial C_i (t,I^{\bullet i})}{\partial I_j^i}
+ \dfrac{\partial D_i (t,e^{\bullet}, I^{\bullet})}{\partial I_j^i} \right)
(I_j^i (t) – I_j^{\bullet i} (t)) \right\} \, \text{d}t \geq 0 \\
\shoveleft {}\mkern5mu
\forall (e,I) \in K(e^\bullet, I^\bullet). \hfill
\end{multline*}