Treatment interaction contrast in a Poisson regression

In a Poisson regression with $\log \mu ={\beta }_0+{\beta }_{T}T+{\beta }_{B}b+{\beta }_{TB}Tb$, the treatment logarithm of the mean ratio at baseline $b$ is ${\beta }_T+b{\beta }_{TB}$. The main treatment coefficient tests the contrast at $b=0$. An overall no-treatment test requires both ${\beta }_T=0$ and ${\beta }_{TB}=0$, with their joint covariance matrix for a Wald test.