Vaccinating to protect a vulnerable subpopulation

Abstract

Background: Epidemic influenza causes serious mortality and morbidity in temperate countries each winter. Research suggests that schoolchildren are critical in the spread of influenza virus, while the elderly and the very young are most vulnerable to the disease. Under these conditions, it is unclear how best to focus prevention efforts in order to protect the population. Here we investigate the question of how to protect a population against a disease when one group is particularly effective at spreading disease and another group is more vulnerable to the effects of the disease.

Methods and findings: We developed a simple mathematical model of an epidemic that includes assortative mixing between groups of hosts. We evaluate the impact of different vaccine allocation strategies across a wide range of parameter values. With this model we demonstrate that the optimal vaccination strategy is extremely sensitive to the assortativity of population mixing, as well as to the reproductive number of the disease in each group. Small differences in parameter values can change the best vaccination strategy from one focused on the most vulnerable individuals to one focused on the most transmissive individuals.

Conclusions: Given the limited amount of information about relevant parameters, we suggest that changes in vaccination strategy, while potentially promising, should be approached with caution. In particular, we find that, while switching vaccine to more active groups may protect vulnerable groups in many cases, switching too much vaccine, or switching vaccine under slightly different conditions, may lead to large increases in disease in the vulnerable group. This outcome is more likely when vaccine limitation is stringent, when mixing is highly structured, or when transmission levels are high.

Figure 1. Complex Tradeoffs in Vaccine Allocation in a Population with Strong Assortative Mixing

The proportion of “vulnerable” (solid lines), and “core” (dashed lines) individuals infected as a function of the proportion of vaccine given to core individuals, for three different transmission scenarios. In low transmission, the value of R for core and vulnerable individuals is 2.0 and 1.2, respectively; in medium transmission R is 2.4 and 1.6; in high transmission R is 2.8 and 2.0. The overall proportion of the population vaccinated is 0.5. The vaccine is assumed to have an efficacy of 80% in protecting core individuals and 50% in protecting vulnerable individuals. The two subpopulations are assumed to be of equal size. The coefficient of preferred mixing used is 0.7 (see Methods).

Figure 2. Vaccine Allocation Tradeoffs in a Population with Weak Assortative Mixing

The proportion of “vulnerable” (solid lines), and “core” (dashed lines) individuals infected as a function of the proportion of vaccine given to core individuals, for three different transmission scenarios. Parameters are the same as in Figure 1, except that the coefficient of preferred mixing used is 0.1 (rather than 0.7).

Figure 3. Parameter Regions with Different Qualitative Responses to Changes in Vaccine Allocation

Insets show vaccine allocation tradeoffs at different points in parameter space, in the style of Figures 1 and 2. Contour lines (solid) separate regions in which the strategy that vaccinates only vulnerable individuals (v) or the one that vaccinates only core individuals (c) is or is not the best (b) or worst (w) on the curve describing changes in incidence in the vulnerable population. Two strategies on a given curve are deemed equivalent if they differ by less than 0.1% of the curve's maximum value. The large region in the middle right shows the case in which neither extreme strategy is best or worst; the extreme properties of any other region are described by the names of the line or lines separating the region from the middle right region. Asterisks correspond to the parameters shown in Figure 1. The dotted line shows values for which R is the same for both groups: our assumption that the core group transmits the disease more effectively than the vulnerable group does not hold in the region above this line.