Purpose: When individuals are at risk for infection from several strains of a virus, but infection by one type precludes infection from another type, uninfected individuals who are immune to one type may be subject to an increased risk of infection from other types. We developed a model of a hypothetical type-specific vaccine to gain qualitative insight into the potential effect of this phenomenon (herein referred to as “risk compensation”) on clinical outcomes.

Methods: An individual-based, dynamic model simulates a cohort with a low prevalence (0.26%) of a hypothetical virus with six types, A-F, characterized according to their risk of mortality: type A is very high-risk, types B-C are high-risk, and types D-F are low-risk. We assume: (1) probabilities of transmission and clearance do not differ by type; (2) mortality risk does vary by type; (3) clearance is associated with lifelong type-specific immunity; (4) vaccination confers complete immunity for types B-C. Infection risks are calculated as a function of prevalence and an individual's immunity profile. We calculated life expectancy (LE) gains with a vaccination program, varying the degree of risk compensation and vaccine efficacy.

Results: Assuming no risk compensation, as vaccination increases, LE increases with diminishing returns and is maximized before 100%. Assuming complete compensation, LE increases with increasing returns. Gradually changing the risk compensation from 0 to 1, the inflexion of the LE curve shifts downwards (see figure). This is due to the fact that without compensation, the high risk types are nearly eliminated by 60% vaccination, whereas with full compensation the spread of high risk types is merely delayed by mid vaccination levels and is only prevented by 100% vaccination.

Conclusion: As expected, compensation blunts the effectiveness of the vaccine, since it increases the risk of the non-vaccinated types, but the change in shape was unanticipated. When modeling vaccines in a setting with multiple types and incomplete data, assumptions about compensation may impact the benefits of vaccination.