After the honeymoon, the divorce: Unexpected outcomes of disease control measures against endemic infections

Author summary Many common endemic infections lack effective, inexpensive vaccinations, and control relies instead on transmission reduction, e.g. mosquito population reduction for dengue. Often, these controls are used with the immediate goal of decreasing the current incidence with little importance placed on what will happen at later points in time, and much less what will happen once the control is stopped. Here, by looking at the cumulative incidence since the beginning of the control period, instead of the instantaneous incidence, we show that when controls are stopped, or fail, the resulting outbreaks can be large enough to completely eliminate any benefit of the control. We call this result thedivorce effect. Further, we show that this result is not limited to specific transmission pathways or epidemiological parameters, but is instead tied directly to the reduction of herd immunity inherent in non-immunizing controls. Lastly, by evaluating programs to minimize the magnitude of the divorce effect, we show that without maintaining herd immunity, or successfully continuing control for decades, it is impossible to keep the costs of post-control outbreaks from outweighing the benefits of the control program. We note that our results have significance in the context of non-pharmaceutical interventions aimed at COVID-19. The lack of effective vaccines for many endemic diseases often forces policymakers to rely on non-immunizing control measures, such as vector control, to reduce the massive burden of these diseases. Controls can have well-known counterintuitive effects on endemic infections, including the honeymoon effect, in which partially effective controls cause not only a greater initial reduction in infection than expected, but also large outbreaks during control resulting from accumulation of susceptibles. Unfortunately, many control measures cannot be maintained indefinitely, and the results of cessation are poorly understood. Here, we examine the results of stopped or failed non-immunizing control measures in endemic settings. By using a mathematical model to compare the cumulative number of cases expected with and without control, we show that deployment of control can lead to a larger total number of infections,counting from the time that control started, than without any control-thedivorce effect. This result is directly related to the population-level loss of immunity resulting from non-immunizing controls and is seen in a variety of models when non-immunizing controls are used against an infection that confers immunity. Finally, we examine three control plans for minimizing the magnitude of the divorce effect in seasonal infections and show that they are incapable of eliminating the divorce effect. While we do not suggest stopping control programs that rely on non-immunizing controls, our results strongly argue that the accumulation of susceptibility should be considered before deploying such controls against endemic infections when indefinite use of the control is unlikely. We highlight that our results are particularly germane to endemic mosquito-borne infections, such as dengue virus, both for routine management involving vector control and for field trials of novel control approaches, and in the context of non-pharmaceutical interventions aimed at COVID-19.