Matrix models can be used to predict population dynamics and assess management options. Invasive trees proliferation within forest ecosystems have not been characterized, hence the need of population dynamics description by use matrix models which is a powerful means of understanding these population structures. Lately, migration, harvesting factors have been incorporated in stage based matrix models for tree population dynamic description. This study seeks to extend the stage based matrix by incorporation of altitudinal, ecological and grazing factors that aids invasion by trees into matrix models with application to the invasive Cestrum auratacium species across different forest blocks ecosystems in Kenya. The study applied an experimental design transects and plots 300m apart nested with sub-plots 10×10m for mature trees, 5×5m for sampling and1×1m for seedling per block. The estimation of eigenvalues, their right and left eigenvectors representing stage structure and reproductive value respectively were determined using the R 3.6.2 program. The results shows the growth rates for Kiptogot =4.84 and Kimothon =3.21, Suam =2.89, Kitale =3.91 and Saboti =3.77. The stable age distribution for life stages for Kimothon was 70.2% seedling, 23.9% sapling, 5.9% mature trees while Kiptogot block was 89.0% seedling, 9.7% sapling, 1.3% mature trees. Suam block was 83.5% seedling, 15.3% sapling, 1.2% mature trees. These results indicate that invasive tree seedling and sampling are increasing in population and have eects on the population of other species within ecosystems. This study provides information that is useful to decision makers in facilitating management of invasive species within the Kenya forest ecosystems.