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Determination of optimal vaccination strategies using an orbital stability threshold from periodically driven systems. (English) Zbl 1282.92020
Summary: We analyse a periodically driven SIR epidemic model for childhood related diseases, where the contact rate and vaccination rate parameters are considered to be periodic. The aim is to define optimal vaccination strategies for the 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 a 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 match periods, we observe some positive effects 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.

MSC:
92C60 Medical epidemiology
49N90 Applications of optimal control and differential games
49J15 Existence theories for optimal control problems involving ordinary differential equations
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