This thesis looked at statistical models for the spread of pneumonia among young children under three in WolaitaSodo town without vaccination. A lung illness known as pneumonia is brought on by bacteria, viruses, or fungi. It is a severe infection where pus and other liquids fill the air sacs. In this research, we use data from the Sodo Town Hospitals to develop a deterministic Susceptible-Exposed-Infectious-Recovered (SEIR) model to study the spread of pneumonia. In this instance, we examine the effects of pneumonia using an Ordinary Differential Equation. The constancy The next generating matrices method was used to analyze the model and find the Basic Reproductive number. If R 0 <1, the disease-free equilibrium is locally asymptotically stable, and if R 0 >1it is unstable. The research assesses the influence of preventative measures (primarily those lacking vaccination) on pneumonia disease. Through the security of the equilibria, conditions for the eradication or persistence of pneumonia infection are deduced. In the event of an outbreak, the most crucial element in stopping the spread of streptococcus pneumonia is prompt vaccination, and vaccination of the susceptible population is necessary to stop the disease’s spread. To support our theoretical findings, numerical simulations are given as a conclusion.