Neighbouring countries need incentives to coordinate disease control, say health policy specialists Ramanan Laxminarayan and colleagues.
The idea that diseases spread across countries, and can therefore be controlled only by transnational arrangements, dates back to at least the mid-1850s, when the first global sanitary conventions were organised in the wake of cholera outbreaks. These conventions recognised that infectious disease control in any single country was possible only with the cooperation of neighbours.
It is no accident that of the 25 countries that eliminated malaria as part of the Global Malaria Eradication Program in the 1950s, 23 were either close neighbours or islands.  The two exceptions were Chile and Israel, both in effect islands the former is physically isolated by high mountains and the latter is demographically isolated for political reasons.
There is now more evidence to suggest that cooperation is crucial.
The usual formula that public health professionals use to determine the vaccination coverage necessary for a disease to be eliminated depends on the reproductive number of the disease. This is an epidemiological variable defined by the number of secondary infections produced by a single infection in a fully susceptible population, that is, the number of previously healthy people infected by a single person already affected by the disease.
Our work incorporates two economic considerations into this model: the cost of vaccination and the cost of disease.  For diseases such as measles, elimination does not relieve the country of the burden of continuing vaccination, and therefore we find that the optimal vaccination level in a country has nothing to do with the reproductive number.
It has everything to do with the economic costs of both vaccination and disease burden.
What is an optimal vaccination strategy? Our model suggests two possibilities: either no vaccination when the cost of coverage is high and the disease is not severe; or elimination when cost is low but the disease burden is high. For mild infections, optimal strategies lie somewhere between these extremes, determined by the relative costs of vaccination and infection.
Next we extended the model to look at optimal vaccination coverage in countries linked by population movement across their borders. If two countries linked in this way cooperate and unite their efforts, they are able to eliminate the disease and so minimise their combined costs of vaccination and disease burden. However, if they act independently, they fail to reach elimination.
Joint and long-lasting funding commitments for vaccination will also enhance herd immunity (a community's collective resistance to infectious disease when the number of susceptible people is low). When countries immunise their local population, as well as help neighbouring countries to reach their targets for elimination, it becomes easier to achieve regional elimination and everyone benefits in the long term.
These findings apply not only to vaccination, but also to any disease control effort that reduces the spread of infectious disease. This suggests that the fight against malaria can be set back significantly in countries that use public health strategies such as insecticides and bednets in areas of low transmission, but have neighbours with high rates of transmission. 
For example, even though Zimbabwe was able to interrupt the transmission of malaria in the 1960s, its proximity to neighbours that did not implement similar efforts has burdened the country with some of the highest levels of malaria in Africa.
Similarly, the global eradication campaign succeeded in decreasing the incidence of malaria in Vietnam, but in the 1980s the disease arrived from neighbouring countries. And in China, although malaria was eliminated from the interior, it continues to be a threat from countries across its southern border.
These examples illustrate that cooperation is essential to combat diseases that cross national borders. This is not restricted to regional control long-term, coordinated efforts that give neighbouring countries an incentive to immunise or put in place other intervention measures can also lead to global elimination of a disease.
Even non-neighbouring countries can experience huge gains from every country's efforts. India's smallpox eradication programme, which was supported by a global effort including the United States, failed initially because of an ineffective strategy, despite the long-term economic incentive. But the United States benefited by not having to carry out in-country vaccinations once smallpox was eradicated worldwide. 
When non-infected countries invest in vaccination efforts for infected countries, enhanced herd immunity in the long term benefits the global population. The Lubombo Spatial Development Initiative, which covered eastern Swaziland, southern Mozambique and the northeastern KwaZulu-Natal province in South Africa, is one example in which a richer country (South Africa) financed the elimination of malaria in poorer countries (Swaziland and Mozambique).
The first step in achieving global benefit is to achieve regional benefits. And since the world is increasingly connected, the benefits of regional control usually extend to non-neighbouring countries for example, by avoiding introductions of malaria from endemic to disease-free regions.
To effectively target diseases that extend across borders, cooperation among countries, external funders and international organisations is essential. In practical terms, this begins with understanding the origins of the disease and is facilitated through coordinated logistical and administrative efforts, long-term funding and targeting disease in infected populations.
The importance of transboundary incentives suggests that malaria elimination, for instance, has as much to do with a neighbouring country's stance against malaria and its effect on the number of incoming cases as the endemic country's control efforts. International programmes should pay attention to these incentives and explicitly consider them in financing measures to control infectious diseases that span countries.
Ramanan Laxminarayan is director of the Center for Disease Dynamics, Economics and Policy in Washington DC, and a research scholar and lecturer at Princeton University in New Jersey, USA. Bryan Grenfell is Kathryn Briger and Sarah Fenton Professor of Ecology and Evolutionary Biology at Princeton University, New Jersey, USA. Petra Klepac is a post-doctoral researcher at the Department of Ecology and Evolutionary Biology at Princeton University, New Jersey, USA.
 Laxminarayan, R. and Smith, D.L. Transnational malaria control and financing (Working paper, CDDEP, 2008)
 Klepac, P. et al. Synthesizing epidemiological and economic optima for control of immunizing infections. Proceedings of the National Academy of Science USA. 23 August. 108(34): 14,366-14,370 (2011)
 Miller, M. et al. Control and eradication. In: Jamison D.T. et al. (eds.) Disease Control Priorities in Developing Countries. 2nd Ed. (World Bank, 2006)