Mathematical Modelling of The Pneumonia Dynamics with a Carrier Among a Children Under Age Five: The Case of Bule Hora Town, Oromia Region, Ethiopia

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Abstract Pneumonia has been a major airborne transmitted disease and continues to pose a major public health problem in both developed and developing countries of the world. In this study, we constructed and analyzed a non-linear deterministic mathematical model in case of Bule Hora town for assessing the community-level impacts of natural immunity, other protection measures and treatment on the transmission dynamics of pneumonia disease in a population of varying size. Our model exhibits two kinds of equilibrium points: pneumonia disease-free equilibrium point, and pneumonia endemic equilibrium point. Thus, for pneumonia infection, the necessity of the pneumonia reproduction number R 0 < 1, although essential, it might not be enough to completely eradicate the pneumonia infection from the considered community. Our examination of sensitivity analysis shows that the pneumonia infection transmission rate plays a crucial role to change the qualitative behavior of dynamics of pneumonia infection. By taking standard data from Bule hora teaching Hospital and published literature, our numerical computations show that the numerical value of pneumonia infection model reproduction number greater than one it implies that the disease spreads throughout the community. Finally, our numerical simulations show that natural immunity and treatment against pneumonia disease have effectively decreasing pneumonia expansion.

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