Optimizing reactive responses to outbreaks of immunizing infections: balancing case management and vaccination

Abstract

For vaccine-preventable infections, immunization generally needs to be supplemented by palliative care of individuals missed by the vaccination. Costs and availability of vaccine doses and palliative care vary by disease and by region. In many situations, resources for delivery of palliative care are independent of resources required for vaccination; however we also need to consider the conservative scenario where there is some trade-off between efforts, which is of potential relevance for resource-poor settings. We formulate an SEIR model that includes those two control strategies--vaccination and palliative care. We consider their relative merit and optimal allocation in the context of a highly efficacious vaccine, and under the assumption that palliative care may reduce transmission. We investigate the utility of a range of mixed or pure strategies that can be implemented after an epidemic has started, and look for rule-of-thumb principles of how best to reduce the burden of disease during an acute outbreak over a spectrum of vaccine-preventable infections. Intuitively, we expect the best strategy to initially focus on vaccination, and enhanced palliative care after the infection has peaked, but a number of plausible realistic constraints for control result in important qualifications on the intervention strategy. The time in the epidemic when one should switch strategy depends sensitively on the relative cost of vaccine to palliative care, the available budget, and R0. Crucially, outbreak response vaccination may be more effective in managing low-R0 diseases, while high R0 scenarios enhance the importance of routine vaccination and case management.

Figure 1. SEIR model with two types of control, vaccination and palliative care.

Infected individuals that receive palliative care form a separate compartment ; vaccination moves individuals from the S compartment to the R compartment, both untreated () and treated () infected individuals may move into mortality compartment (D), according to their respective case fatality rates.

Figure 2. Proportion of lives saved compared to the baseline case over the range of intensities of vaccination (y-axis) and palliative care (x-axis) in simulated epidemics for different times of onset of control implementation.

Red colors represent higher effectiveness. Bottom graph shows the epidemic curves for the uncontrolled case; the vertical lines show the days of the outbreak for which we implement control (vaccination and palliative care) in relation to the peak of the epidemic. The model is parameterized according to the 2003–2004 measles outbreak among children in Niamey. Parameter values: , days, days, year⁻¹, , .

Figure 3. Proportion of lives saved compared to the case where control is implemented.

Blue line shows the vaccination-only strategy, black line shows case-management-only strategy, and gray shows a range of mixed strategies where both vaccination and palliative care are used simultaneously and the budget is split the two, vertical line shows where the infection peaks. Columns from left to right show increasing budget values, whereas rows show increasing per capita cost of vaccine to palliative care ratio (). Columns show increasing budget levels (from left to right: , , dimensionless units of cost). , , , days, days, days, year⁻¹, , , .

Figure 4. Optimal strategies over a range of

values. (A) The time in the outbreak when the strategy should be switched from vaccine-only to a palliative-care-only strategy, for 3 ratios of costs of unit palliative care and unit vaccine: 1, 10, 100 (curves from left to right, dark green, light green, and yellow, respectively). Time is rescaled to epidemic time (in relation to the duration of the epidemic that changes with ) so that outbreaks for all values of peak along the vertical black line. (B)–(D) Best performing strategy over a range of values and different times of control. The colorbar shows the proportion of the budget invested in palliative care; 0 (dark blue) is vaccination-only strategy, 1 (dark red) is palliative-care-only strategy. Red colors correspond to palliative-care-intense strategies, and strategies in the blue region focus on vaccination. Time is rescaled to the epidemic so that for all values the epidemic peaks along the black line. The white line shows the time at which one should switch from a vaccine-only to a palliative-care-only strategy in (A). In (B) the cost of per unit palliative care () is equal to per unit cost of vaccine (),  = ; (C)  = 10 ; (D)  = 100 . Limited budget (100000 cost units). Outbreak alert threshold is set to 10 cases. Parameters: , and are varied according to such that , days, days, days, year⁻¹, , , .