In this article, a spatiotemporal dynamical system model (tree model) is utilized for investigating the features of forced and unforced turbulence in a dispersed phase two-phase system. The tree model includes a variable for spatial dimension in addition to variables of wavenumber and time, which display both spatial and temporal intermittencies. The focus of this paper is to study the turbulence modulation due to the presence of rigid particles. The study considers particles with the sizes of 32, 64, and 128 times the Kolmogorov length scale. Specifically, the study of the energy dissipation rate (EDR) at the particle-fluid interface is considered. Two models, namely, A and B with different types of interaction connections between nearby shells, are used first to compare the results of the particle-laden case with decaying turbulence. The number of tree connections in the model is found to affect the amount of augmentation of EDR near the particle surface. Model B is studied further with different sizes of particles in forced turbulence cases and compared to the unladen case with the same parameters. Also, the model expression is studied in the forced turbulence case of dual particles separated by given distances. The results of spatiotemporal shell models provide new approach of handling high Reynolds turbulence in dispersed phase multiphase systems.