In this thesis, different types of systems are studied to investigate the effects of the environmental factors on diffusion and transfer time. Each system consists of different energy levels and excitation transfers between them. The mismatch between the energy levels leads to the Anderson localization. Localization has a negative effect on transport. It is shown that Anderson localization is suppressed due to interaction with the environment. To describe the dynamical evolution of the open quantum system Lindblad master equation is used. The transition times of the system from the pure state to the completely mixed state are examined with the help of the density matrix. In consequence of our study, because of the interaction between the system and environment the change in the wavefunction, the loss in the interference terms and an irreversible information flow in the total system are observed. Destructive effects of the environmental noise on localization are observed for different scenarios and diffusion enhanced. However, when the interaction with the environment becomes larger than a critical value, the system exhibits Zeno effect. In the Zeno regime, the time evolution of the quantum state of the system as well as the diffusion is suppressed.