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Self-enforcing regional vaccination agreements.

Klepac P, Megiddo I, Grenfell BT, Laxminarayan R - J R Soc Interface (2016)

Bottom Line: Mobility of populations across borders can promote free-riding, because a country can benefit from the vaccination efforts of its neighbours, which can result in vaccination coverage lower than the global optimum.We find that countries can achieve significantly greater vaccination coverage at a lower cost by forming coalitions than when acting independently, provided a coalition has the tools to deter free-riding.Furthermore, when economically or epidemiologically asymmetric countries form coalitions, realized coverage is regionally more consistent than in the absence of coalitions.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK pklepac@alum.mit.edu.

No MeSH data available.


Related in: MedlinePlus

Overall coalition savings when a coalition becomes a fully cooperative coalition (all countries participate, k = n), with a country that joins the coalition last indicated on the x-axis. Parameter values as in figure 4.
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RSIF20150907F5: Overall coalition savings when a coalition becomes a fully cooperative coalition (all countries participate, k = n), with a country that joins the coalition last indicated on the x-axis. Parameter values as in figure 4.

Mentions: In a fully cooperative outcome (figure 4 green lines), optimal vaccine coverage is considerably higher particularly for the countries with previously low coverage (e.g. compare red and green lines in figure 4 for country 1: vaccination coverage increases from 0 to greater than 30%). The cost of elevating coverage for these countries is high, but the savings of their neighbours through avoided infections more than compensate for these costs. As more countries join the coalition, the vaccination coverage among signatories increases (figure 4b, black circles) and approaches the global optimum (figure 4b, green lines). Coverage among non-signatories (figure 4b grey dots) remains comparable to the non-cooperative outcome (figure 4b red lines) although they enjoy slightly lowered costs owing to free-riding (figure 4a, grey dots). Compared with the non-cooperative outcome (figure 4b, red lines), differences in coverage levels and prevalence decrease as the coalition approaches full cooperation (figure 4b,c, note the decreased range of green compared with than red lines; see also electronic supplementary material, figure S6 where reductions in prevalence are achieved at very little cost). Overall, the fully cooperative coalition achieves higher vaccination coverage at a lower cost than smaller coalitions, with some countries benefiting more than others (figure 4a and see also electronic supplementary material, figure S4). Countries with low perceived cost of infection (countries 1 and 2 in figure 4a) experience an increase in their costs compared with non-cooperative outcome. If overall costs of the coalition decrease when it becomes fully cooperative (all countries are members), then its members can promote participation by compensating the countries that would otherwise incur an increase in costs. The coalition can become fully cooperative in eight different ways—each respective country can be the last one to join. Because of asymmetries in parameter values, the costs incurred when increasing the size of the coalition from seven to eight members will differ in each of these scenarios. Regardless of which country joins the coalition last the overall benefit of the coalition is positive (figure 5), even though some countries can incur a cost from joining a coalition (electronic supplementary material, figure S7). With heterogeneity, the differences in incurred or perceived costs between countries have the potential to be used as compensation to increase coalition participation, leading to elevated and more consistent vaccination coverage in the region.Figure 5.


Self-enforcing regional vaccination agreements.

Klepac P, Megiddo I, Grenfell BT, Laxminarayan R - J R Soc Interface (2016)

Overall coalition savings when a coalition becomes a fully cooperative coalition (all countries participate, k = n), with a country that joins the coalition last indicated on the x-axis. Parameter values as in figure 4.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4759795&req=5

RSIF20150907F5: Overall coalition savings when a coalition becomes a fully cooperative coalition (all countries participate, k = n), with a country that joins the coalition last indicated on the x-axis. Parameter values as in figure 4.
Mentions: In a fully cooperative outcome (figure 4 green lines), optimal vaccine coverage is considerably higher particularly for the countries with previously low coverage (e.g. compare red and green lines in figure 4 for country 1: vaccination coverage increases from 0 to greater than 30%). The cost of elevating coverage for these countries is high, but the savings of their neighbours through avoided infections more than compensate for these costs. As more countries join the coalition, the vaccination coverage among signatories increases (figure 4b, black circles) and approaches the global optimum (figure 4b, green lines). Coverage among non-signatories (figure 4b grey dots) remains comparable to the non-cooperative outcome (figure 4b red lines) although they enjoy slightly lowered costs owing to free-riding (figure 4a, grey dots). Compared with the non-cooperative outcome (figure 4b, red lines), differences in coverage levels and prevalence decrease as the coalition approaches full cooperation (figure 4b,c, note the decreased range of green compared with than red lines; see also electronic supplementary material, figure S6 where reductions in prevalence are achieved at very little cost). Overall, the fully cooperative coalition achieves higher vaccination coverage at a lower cost than smaller coalitions, with some countries benefiting more than others (figure 4a and see also electronic supplementary material, figure S4). Countries with low perceived cost of infection (countries 1 and 2 in figure 4a) experience an increase in their costs compared with non-cooperative outcome. If overall costs of the coalition decrease when it becomes fully cooperative (all countries are members), then its members can promote participation by compensating the countries that would otherwise incur an increase in costs. The coalition can become fully cooperative in eight different ways—each respective country can be the last one to join. Because of asymmetries in parameter values, the costs incurred when increasing the size of the coalition from seven to eight members will differ in each of these scenarios. Regardless of which country joins the coalition last the overall benefit of the coalition is positive (figure 5), even though some countries can incur a cost from joining a coalition (electronic supplementary material, figure S7). With heterogeneity, the differences in incurred or perceived costs between countries have the potential to be used as compensation to increase coalition participation, leading to elevated and more consistent vaccination coverage in the region.Figure 5.

Bottom Line: Mobility of populations across borders can promote free-riding, because a country can benefit from the vaccination efforts of its neighbours, which can result in vaccination coverage lower than the global optimum.We find that countries can achieve significantly greater vaccination coverage at a lower cost by forming coalitions than when acting independently, provided a coalition has the tools to deter free-riding.Furthermore, when economically or epidemiologically asymmetric countries form coalitions, realized coverage is regionally more consistent than in the absence of coalitions.

View Article: PubMed Central - PubMed

Affiliation: Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, UK pklepac@alum.mit.edu.

No MeSH data available.


Related in: MedlinePlus