The inner trapped particles in the radiation belts could harm to low Earth orbit (LEO) satellites. Although the population of inner radiation belts is usually stable, its response to extreme large solar and geomagnetic events can produce satellite anomalies. The risk is higher because of the frequent LEO satellite passes through the South Atlantic Anomaly (SAA). To accomplish that matter, a model for forecasting the distribution of trapped particle fluxes in equatorial LEO based on the hierarchical Bayesian spatio-temporal (HBST) statistical model was developed. This model is applicable to low- and medium-energy electrons and protons in all conditions of solar activity. The dynamic rather than static data were also used. A simple HBST model which is named Gaussian process (GP) was developed using the NOAA 15-17 data, which categorized particle energies as > 30 keV (mep0e1) and > 300 keV (mep0e3) for electrons and 80-240 keV (mep0p2) and 800-2500 keV (mep0p4) for protons in the SAA region. The goal of this study was to examine the applicability of this model during a quiet period (15-19 May 2009) and a period of high solar activity (26-30 October 2003). The forecast was then interpolated using a Kriging technique to estimate the particle distribution. Statistical and visual validations showed good indicators, with average mean relative error (MRE) values of 20-30% for both periods and a similar pattern to that of the National Oceanic and Atmospheric Administration (NOAA) map. Based on the results, this work contributes a method for predicting the trapped particle flux distribution at low latitude LEOs.