  We investigate the type of dual superconductivity responsible for quark
confinement. For this purpose, we solve the field equations of the $U(1)$
gauge-scalar model to obtain the static vortex solution in the whole range
without restricting to the long-distance region. Then we use the resulting
magnetic field of the vortex to fit the gauge-invariant chromoelectric field
connecting a pair of quark and antiquark which was measured by numerical
simulations for $SU(2)$ Yang--Mills theory on a lattice. This result improves
the accuracy of the fitted value for the Ginzburg--Landau parameter to
reconfirm the type I dual superconductivity for quark confinement which was
claimed by preceding works based on a fitting using the Clem ansatz. Moreover,
we calculate the Maxwell stress tensor to obtain the distribution of the force
around the flux tube. This result suggests that the attractive force acts among
chromoelectric flux tubes, in agreement with the type I dual superconductivity.
