Pneumonia is mainly caused by bacteria called Streptococcus Pneumoniae. It is one of the leading causes of mortality among children in the developing countries claiming about 1.9 million lives per year. Deaths due to pneumonia can occur within 3 days of illness and any delay of treatment may not save live. Hence prompt and effective control measures for the disease is needed. Integrating mathematical modeling in epidemiological research is important in studying dynamics and identifying effective control measures. We developed mathematical models by applying the theory of ordinary differential equations and dynamical systems to study the dynamics of pneumonia and assessed the optimal control strategy in a community. Finally, a Monte Carlo Markov Chain (MCMC) simulation technique was used to simulate data for transmission parameters when vaccination and treatment are used as control strategies. A kernel density estimation was then used to estimate probability distribution of the transmission parameters. The results show that eliminating carriers in a population, case detection and use of both vaccination and treatment is an important strategy in reducing the disease dynamics.