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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

SIR model for a system of eight asymmetric interconnected countries showing summary statistics for costs (a), coverage (b) or prevalence (c). For each country (shown on x-axis in black), the coalition sizes (indicated in grey on x-axis) are ordered from 1 (non-cooperative outcome) to 8 (fully cooperative outcome). There are  possible coalitions of size k, and here we show the mean value and range of optimization outcomes for a given country in a coalition of a given size. Circles show mean costs (a), coverage (b) or prevalence (c) for each country and each coalition size when that country is in coalition (black) and outside of coalition (grey). Whiskers show fifth and 95th quantiles. Red and green lines show independent and global optimum for each country, respectively. Cost of infection parameter varies linearly across countries from cI1 = 1 for country 1, and cI8 = 15 for country 8. R0 = 5, coupling strength = 10μ/(n − 1), ai = 0.1. All 248 optimizations are shown in electronic supplementary material, figure S4.
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RSIF20150907F4: SIR model for a system of eight asymmetric interconnected countries showing summary statistics for costs (a), coverage (b) or prevalence (c). For each country (shown on x-axis in black), the coalition sizes (indicated in grey on x-axis) are ordered from 1 (non-cooperative outcome) to 8 (fully cooperative outcome). There are possible coalitions of size k, and here we show the mean value and range of optimization outcomes for a given country in a coalition of a given size. Circles show mean costs (a), coverage (b) or prevalence (c) for each country and each coalition size when that country is in coalition (black) and outside of coalition (grey). Whiskers show fifth and 95th quantiles. Red and green lines show independent and global optimum for each country, respectively. Cost of infection parameter varies linearly across countries from cI1 = 1 for country 1, and cI8 = 15 for country 8. R0 = 5, coupling strength = 10μ/(n − 1), ai = 0.1. All 248 optimizations are shown in electronic supplementary material, figure S4.

Mentions: For each population i, we distinguish between costs of vaccination c(pi), that capture immunization programmes' implementation and operation costs and increase exponentially with the proportional increase in vaccination coverage (as supported by data, e.g. see figure 4 in [18]), and infection costs cIi that capture direct and indirect costs of disease (e.g. morbidity, mortality and loss of productivity) and so are proportional to the equilibrium prevalence of infection [4],3.3with the total cost3.4


Self-enforcing regional vaccination agreements.

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

SIR model for a system of eight asymmetric interconnected countries showing summary statistics for costs (a), coverage (b) or prevalence (c). For each country (shown on x-axis in black), the coalition sizes (indicated in grey on x-axis) are ordered from 1 (non-cooperative outcome) to 8 (fully cooperative outcome). There are  possible coalitions of size k, and here we show the mean value and range of optimization outcomes for a given country in a coalition of a given size. Circles show mean costs (a), coverage (b) or prevalence (c) for each country and each coalition size when that country is in coalition (black) and outside of coalition (grey). Whiskers show fifth and 95th quantiles. Red and green lines show independent and global optimum for each country, respectively. Cost of infection parameter varies linearly across countries from cI1 = 1 for country 1, and cI8 = 15 for country 8. R0 = 5, coupling strength = 10μ/(n − 1), ai = 0.1. All 248 optimizations are shown in electronic supplementary material, figure S4.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

RSIF20150907F4: SIR model for a system of eight asymmetric interconnected countries showing summary statistics for costs (a), coverage (b) or prevalence (c). For each country (shown on x-axis in black), the coalition sizes (indicated in grey on x-axis) are ordered from 1 (non-cooperative outcome) to 8 (fully cooperative outcome). There are possible coalitions of size k, and here we show the mean value and range of optimization outcomes for a given country in a coalition of a given size. Circles show mean costs (a), coverage (b) or prevalence (c) for each country and each coalition size when that country is in coalition (black) and outside of coalition (grey). Whiskers show fifth and 95th quantiles. Red and green lines show independent and global optimum for each country, respectively. Cost of infection parameter varies linearly across countries from cI1 = 1 for country 1, and cI8 = 15 for country 8. R0 = 5, coupling strength = 10μ/(n − 1), ai = 0.1. All 248 optimizations are shown in electronic supplementary material, figure S4.
Mentions: For each population i, we distinguish between costs of vaccination c(pi), that capture immunization programmes' implementation and operation costs and increase exponentially with the proportional increase in vaccination coverage (as supported by data, e.g. see figure 4 in [18]), and infection costs cIi that capture direct and indirect costs of disease (e.g. morbidity, mortality and loss of productivity) and so are proportional to the equilibrium prevalence of infection [4],3.3with the total cost3.4

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