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Modelling Transmission Dynamics of Childhood Diseases in the Presence of a Preventive Vaccine: Application of Adomian Decomposition Technique

In: Mathematical Modeling, Simulation, Visualization and e-Learning

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  • O. D. Makinde

Abstract

In recent time, diligent vaccination campaigns have resulted in high levels of permanent immunity against the childhood disease among the population, e.g.measles, mumps, rubella, poliomyelitis, etc. In this paper, a SIR model that monitors the temporal dynamics of a childhood disease in the presence of a preventive vaccine is developed. The qualitative analysis reveals the vaccination reproductive number for disease control and eradication. Adomian decomposition method is also employed to compute an approximation to the solution of the non-linear system of differential equations governing the problem. Graphical results are presented and discussed quantitatively to illustrate the solution.

Suggested Citation

  • O. D. Makinde, 2008. "Modelling Transmission Dynamics of Childhood Diseases in the Presence of a Preventive Vaccine: Application of Adomian Decomposition Technique," Springer Books, in: Dialla Konaté (ed.), Mathematical Modeling, Simulation, Visualization and e-Learning, pages 63-74, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-74339-2_5
    DOI: 10.1007/978-3-540-74339-2_5
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