We consider two neighbouring countries in which a pandemic disease spreads. Countries face a trade-off between the social costs of the epidemic diffusion and the monetary costs in order to avoid the insurgence of pandemics. However, due to migration of people across countries, the treatment efforts by one country generate a positive externality for the neighbouring country. Both countries can negotiate on the healthcare cost that each has to sustain. But, they do so subject to a central authority (CA) who can impose penalties to both countries whenever they cannot reach an agreement. We analyse the outcome of such situation via the Nash bargaining concept. Next we show how the CA should design penalties to i) ensure that revealing the true migration flow data is a self-enforcing behaviour, and to ii) enforce that the NB solution adheres to certain fairness properties.