Epidemiological, evolutionary, and economic determinants of eradication tails.

Despite modern medical interventions, infectious diseases continue to generate huge socio-economic losses. The benefits of eradicating a disease are therefore high. While successful with smallpox and rinderpest, many other eradication attempts have failed. Eradications require huge and costly efforts, which can be sustained only if sufficient progress can be achieved. While initial successes are usually obtained more easily, progress often becomes harder as a disease becomes rare in the eradication endgame. A long eradication tail of slowly decreasing incidence levels can frustrate eradication efforts, as it becomes unclear whether progress toward eradication is still being made and how much more needs to be invested to push the targeted disease beyond its extinction threshold. Realistic disease dynamics are complicated by evolutionary responses to interventions and by interactions among different temporal and spatial scales. Models accounting for these complexities are required for understanding the shapes of eradication tails. In particular, such models allow predicting how hard or costly eradication will be, and may even inform in which manner progress has to be assessed during the eradication endgame. Here we outline a general procedure by analyzing the eradication tails of generic SIS diseases, taking into account two major ingredients of realistic complexity: a group-structured host population in which host contacts within groups are more likely than host contacts between groups, and virulence evolution subject to a trade-off between host infectivity within groups and host mobility among groups. Disentangling the epidemiological, evolutionary, and economic determinants of eradication tails, we show how tails of different shapes arise depending on salient model parameters and on how the extinction threshold is approached. We find that disease evolution generally extends the eradication tail and show how the cost structure of eradication measures plays a key role in shaping eradication tails.