Abstract:
Pneumonia is an infection of the lungs that is caused by bacteria, viruses, fungi, or parasites. For a long
time to the best of our knowledge there have not been reliable mathematical model for childhood
pneumonia in Kenya. This research study developed a deterministic model based on the Susceptible-
Vaccinated-Infected-Treated-Recovered-Susceptible compartment classes. The study used the partial
differentiation of control reproduction number toinvestigate effects of; environment, efficacy of
vaccination drug and treatment. Model analysis indicates the system lie in feasible region, it is bounded,
has no backward bifurcation and there exists unique endemic equilibrium point when control
reproduction number is greater than unity. Local and global stability of the equilibrium points indicated
that control reproduction has to be maintained at less than unity to eradicate the disease. Sensitivity
analysis of the control reproduction number indicates that improved vaccination drug’s efficacy, attaining
herd immunity, higher treatment rates and lower effects of environment are the best intervention
strategies to lower impact of the pneumonia of the children under the age of five years in Kenya.
