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J Math Biol. 2014 Feb;68(3):763-84. doi: 10.1007/s00285-013-0648-8. Epub 2013 Feb 14.

Determination of optimal vaccination strategies using an orbital stability threshold from periodically driven systems.

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School of Mathematics, University of Nairobi, Box 30197-00100, Nairobi, Kenya,


We analyse a periodically driven SIR epidemic model for childhood related diseases, where the contact rate and vaccination rate parameters are considered periodic. The aim is to define optimal vaccination strategies for control of childhood related infections. Stability analysis of the uninfected solution is the tool for setting up the control function. The optimal solutions are sought within a set of susceptible population profiles. Our analysis reveals that periodic vaccination strategy hardly contributes to the stability of the uninfected solution if the human residence time (life span) is much larger than the contact rate period. However, if the human residence time and the contact rate periods match, we observe some positive effect of periodic vaccination. Such a vaccination strategy would be useful in the developing world, where human life spans are shorter, or basically in the case of vaccination of livestock or small animals whose life-spans are relatively shorter.

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