SEITR model formulation

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I would like to formulate a SEITR model with infectivity in the exposed period and treatment. What I did is something like this: \begin{align*} S'&= -bS(I+eE+dT)\\ E' &= bS(I+eE+dT) -(a+c)E\\ I' &= aE - kI\\ T'&= cE -nT\\ R'&= kI +nT\\ \end{align*} Is this valid?