  We divide the cross section for a meson-meson reaction into three parts. The
first part is for the quark-interchange process, the second for quark-antiquark
annihilation processes and the third for resonant processes. Master rate
equations are established to yield time dependence of fugacities of pions,
rhos, kaons and vetor kaons. The equations include cross sections for inelastic
scattering of pions, rhos, kaons and vector kaons. Cross sections for
quark-interchange-induced reactions, that were obtained in a potential model,
are parametrized for convenient use. The number densities of pion and rho (kaon
and vector kaon) are altered by quark-interchange processes in equal magnitudes
but opposite signs. The master rate equations combined with the hydrodynamic
equations for longitudinal and transverse expansion are solved with many sets
of initial meson fugacities. Quark-interchange processes are shown to be
important in the contribution of the inelastic meson-meson scattering to
evolution of mesonic matter.
