Optimal vaccination strategies in periodic setting
Researchers:
Nelson Onyango
The project aims are obtaining optimal vaccination strategies for childhood diseases in periodic settings. We characterize vaccination for childhood diseases as follows: One, childhood diseases are periodic due to school year or seasonal effects such a climate influencing the force of infection in a periodic manner. Two, vaccination strategies are characterized by cost constraints. Three, childhood diseases evolve on a faster time scales compared to population dynamics. The standard mathematical approach for periodically driven systems is Floque't-theory, which examines orbital stability. We conjecture that results of Floquet theory are inept for stability studies involving models of childhood diseases. One, because Floquet theory is not suited for systems with different time scales. Two, orbital stability is an averaging criterion and may not trace small outbreaks in disease. Instantaneous stability analysis along the orbits would be more informative. The mathematical tools used to define optimal vaccination strategies were developed by Mueller (1998) and later publications, together with concepts of pulse vaccination strategy, e.g., by Agur et al. (1993), Shulgin et al. (1998).
References
• Z. Agur, L. Cojocaru, G. Mazor, R. Anderson, and Y. Danon, Pulse mass measles vaccination across age cohorts, Proc. Natl. Acad. Sci. 90 (1993), 11698-11702.
• J. Mueller, Optimal vaccination patterns in age-structured populations, SIAM J. Appl. Math. 59 (1998), 222-241.
• B. Shulgin, L. Stone, and Z. Agur, Pulse vaccination strategy in the SIR epidemic model, Bull. Math. Biol. 60 (1998), 1123-1148.
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