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Researchers should cite this work as follows:

• Winkel, B. (2023). 2011-Cruz-Aponte-Herrera-Valdez-Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administrati. SIMIODE, QUBES Educational Resources. doi:10.25334/PRY6-EG24

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Cruz-Aponte, Maytee, Erin C McKiernan1, Marco A Herrera-Valdez. 2011. Mitigating effects of vaccination on influenza outbreaks given constraints in stockpile size and daily administration capacity. BMC Infectious Diseases. 11:207. 16 pp.

See https://bmcinfectdis.biomedcentral.com/articles/10.1186/1471-2334-11-207. Accessed 28 March 2023.

Abstract: "Background: Influenza viruses are a major cause of morbidity and mortality worldwide. Vaccination remains a powerful tool for preventing or mitigating influenza outbreaks. Yet, vaccine supplies and daily administration capacities are limited, even in developed countries. Understanding how such constraints can alter the mitigating effects of vaccination is a crucial part of influenza preparedness plans. Mathematical models provide tools for government and medical officials to assess the impact of different vaccination strategies and plan accordingly. However, many existing models of vaccination employ several questionable assumptions, including a rate of vaccination proportional to the population at each point in time.

“Methods: We present a SIR-like model that explicitly takes into account vaccine supply and the number of vaccines administered per day and places data-informed limits on these parameters. We refer to this as the nonproportional model of vaccination and compare it to the proportional scheme typically found in the literature.

“Results: The proportional and non-proportional models behave similarly for a few different vaccination scenarios. However, there are parameter regimes involving the vaccination campaign duration and daily supply limit for which the non-proportional model predicts smaller epidemics that peak later, but may last longer, than those of the proportional model. We also use the non-proportional model to predict the mitigating effects of variably timed vaccination campaigns for different levels of vaccination coverage, using specific constraints on daily administration capacity.

“Conclusions: The non-proportional model of vaccination is a theoretical improvement that provides more accurate predictions of the mitigating effects of vaccination on influenza outbreaks than the proportional model. In addition, parameters such as vaccine supply and daily administration limit can be easily adjusted to simulate conditions in developed and developing nations with a wide variety of financial and medical resources. Finally, the model can be used by government and medical officials to create customized pandemic preparedness plans based on the supply and administration constraints of specific communities.”

Keywords: SIR, epidemic, infection, vaccination, outbreak,  stability, equilibrium, model, differential equation, system, nonlinear