The most efficient critical vaccination coverage and its equivalence with maximizing the herd effect

Evelot Westerink-Duijzer, Willem van Jaarsveld, Jacco Wallinga and Rommert Dekker

No EI2016-06, Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute

Abstract: ‘Critical vaccination coverages’ are vaccination allocations that result in an effective reproduction ratio of one. In a population with interacting subpopulations there are many different critical vaccination coverages. To find the most efficient critical vaccination coverage, we define the following optimization problem: minimize the required amount of vaccines to obtain an effective reproduction ratio of exactly one. We prove that this optimization problem is equivalent to the problem of maximizing the proportion of susceptibles that escape infection during an epidemic (i.e., maximizing the herd effect). We propose an efficient general algorithm to solve these optimization problems based on Perron- Frobenius theory. We study two special cases that provide further insight into these optimization problems. First, we derive an explicit analytic solution for the case of two interacting populations. Second, we derive an efficient algorithm for the case of multiple populations that interact according to separable mixing. In this algorithm the subpopulations are ordered by their ratio of population size to reproduction ratio. Allocating vaccines based on this priority order results in an optimal allocation. We apply our solutions in a case study for pre-pandemic vaccination in the initial phase of an influenza pandemic where the entire population is susceptible to the new influenza virus. The results show that for the optimal allocation the critical vaccination coverage is achieved for a much smaller amount of vaccines as compared to allocations proposed previously.

Keywords: infectious diseases; vaccination; reproduction number; heterogeneous mixing; optimization; mathematical model (search for similar items in EconPapers)
Pages: 36
Date: 2016-02-18
New Economics Papers: this item is included in nep-hea
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

Downloads: (external link)
https://repub.eur.nl/pub/79912/EI2016-06.pdf (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ems:eureir:79912

Access Statistics for this paper

More papers in Econometric Institute Research Papers from Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute Contact information at EDIRC.
Bibliographic data for series maintained by RePub ( this e-mail address is bad, please contact ).