In an ideal world, there should never be a trade-off between the extent and timing of palliative care and vaccination. There would be enough vaccine doses for everyone (ideally given prophylactically before epidemics), with infrastructure that ensured rapid delivery; furthermore all infected cases who were not immunized would get appropriate and timely treatment. However, vaccination sometimes needs to be given reactively, and, in some circumstances there may be a trade off between vaccination and palliative care. Here we try to identify general rules for how to best make those decisions in the worst case scenarios of constraints between different interventions.
We use a SEIR-type model for acute immunizing infections inspired by measles epidemiology, and explore it over a wide range of epidemiological parameters thereby encompassing other infections such as mumps, rubella, influenza. The model is a simple one, without any heterogeneity in transmission, demography or space, but our preliminary analysis provides important insight into the efficacy and robustness of common reactive control strategies: palliative care and vaccination. In the simplest analysis without budget constraints, outbreak response vaccination is an effective way of reducing mortality and morbidity, especially if vaccination starts early in the outbreak. As a general rule one should vaccinate as much as possible early in the outbreak, and then switch to palliative care after the infection has peaked.
In the presence of budget limitation and logistic constraints (e.g. uncertainty in outbreak detection, or delays in control introduction) the best strategy is inconsistent with that expected in the simplest case. For high
palliative care becomes optimal even before the peak; and for low
palliative care may not be particularly beneficial when implemented after the peak. The more affordable the palliative care, the more effective it becomes earlier in an outbreak up to a limit of vaccine efficacy - early in an outbreak, vaccine is always most effective, since the number of cases we can avert by vaccination is larger than the number of deaths prevented with case management. For high
diseases the rate of spread of the infection soon becomes faster than the rate of immunization - reactive vaccination is no longer an effective way of controlling an outbreak in this case, and the focus should be on routine vaccination and palliative care.
Uncertainty in the timing of the outbreak, or introduction of the control measures later in the outbreak slightly shifts the optimal strategy to a mixed palliative care and vaccination strategy, and then to an entirely palliative care strategy after the epidemic has peaked. At the beginning of the outbreak it is unlikely that a true value of
is known. Here we have presented the simplest case. In practice, a number of intricacies will complicate the picture; for example, age and contact-structure, e.g.
[7],
[43]–
[45], space
[33],
[46],
[47], recurrent epidemics and pathogen life history. Since our focus is on managing a single outbreak, our epidemic model does not include a discount factor for the value of future infections. Discount rates can change the nature of the optimal strategy for disease control
[12],
[48],
[49] and as such should be considered for determining long-term control strategies.
For small
infections and perfect vaccine, vaccination alone is enough to interrupt the chain of transmission and contain the outbreak. Seasonal influenza has a low effective reproduction ratio of infection,
[50], so we would expect immunizations programs alone to be the best strategy for control. However, in reality, the flu vaccine is imperfect and the virus adapts to escape prevailing immunity, so that multiple vaccinations are required for protection. This can lead to variation in repeat vaccine efficacy because of differences in antigenetic distances among vaccine strains and between the vaccine strains and the epidemic outbreak strain
[51]. Such reductions in vaccine efficacy will put more importance on indirect protection via palliative care.
In cases where the detection methods fail to recognize the outbreak early, the opportunity to interrupt the transmission with the direct and indirect protection offered by vaccination is missed, so the best control strategy is intense case management (palliative care) even at low
. This emphasizes that a key issue in successful outbreak control is early detection and rapid response
[52]. Improving detection methods and lowering the threshold for outbreak alert to only a few infected cases is essential for transmission interruption. For logistic reasons there are certain delays associated with outbreak responses. Lowering threshold alerts to just one detected case for measles (as suggested by WHO Communicable disease profile for Niger,
[53]) could provide indispensable time that would allow control measures to be implemented early enough to stop transmission.
Operational realities are inevitably more complex than the framework presented here, and in particular, the source of budgets for vaccination vs. palliative care may be rather different, and thus not reflect the trade-off implemented here. However, overall, our results provide a strategic view of how information on timeliness and budget and logistic constraints, as well as characteristics of the infection, like
, affect the most effective intervention for immunizing infections.
. Crucially, outbreak response vaccination may be more effective in managing low-
diseases, while high 
scenarios enhance the importance of routine vaccination and case management.
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