Mathematical model for pneumonia dynamics among children
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The 2012 Southern Africa mathematical sciences association Conference (SAMSA 2012)26th -29th Nov 2012
There are major advances which have been made to understand the epidemiology of infectious diseases. However, more than 2 million children in the developing countries still die from pneumonia each year. The eorts to promptly detect, eectively treat and control the spread of pneumonia is possible if its dynamics is understood. In this paper,we develop a mathematical model for pneumonia among children underve years of age. The model is analyzed using the theory of ordinary dierential equations and dynamical systems. We derive the basic reproduction number, R0, analyze the stability of equilibrium points and bifurcation analysis. The results of the analysis shows that there exist a locally stable disease free equilibrium point, Ef when R0 < 1 and a unique endemic equilibrium, Ee when R0 > 1.The analysis also shows that there is a possibility of a forward bifurcation.
There are major advances which have been made to understand the epidemiology of infectious diseases. However, more than 2 million children in the developing countries still die from pneumonia each year. The eorts to promptly detect, eectively treat and control the spread of pneumonia is possible if its dynamics is understood. In this paper,we develop a mathematical model for pneumonia among children underve years of age. The model is analyzed using the theory of ordinary dierential equations and dynamical systems. We derive the basic reproduction number, R0, analyze the stability of equilibrium points and bifurcation analysis. The results of the analysis shows that there exist a locally stable disease free equilibrium point, Ef when R0 < 1 and a unique endemic equilibrium, Ee when R0 > 1.The analysis also shows that there is a possibility of a forward bifurcation.
Keywords
Pneumonia Model, Basic reproduction number, forward bifurcation, Stability, Carriers