Waning Immunity Is Associated with Periodic Large Outbreaks of Mumps: A Mathematical Modeling Study of Scottish Data

Abstract

Vaccination programs for childhood diseases, such as measles, mumps and rubella have greatly contributed to decreasing the incidence and impact of those diseases. Nonetheless, despite long vaccination programmes across the world, mumps has not yet been eradicated in those countries: indeed, large outbreaks continue. For example, in Scotland large outbreaks occurred in 2004, 2005, and 2015, despite introducing the MMR (Measles-Mumps-Rubella) vaccine more than 20 years ago. There are indications that this vaccine-preventable disease is re-emerging in highly vaccinated populations. Here we investigate whether the resurgence of mumps is due to waning immunity, and further, could a booster dose be the solution to eradicate mumps or would it just extend the period of waning immunity? Using mathematical modeling we enhance a seasonally-structured disease model with four scenarios: no vaccination, vaccinated individuals protected for life, vaccinated individuals at risk of waning immunity, and introduction of measures to increase immunity (a third dose, or a better vaccine). The model is parameterised from observed clinical data in Scotland 2004-2015 and the literature. The results of the four scenarios are compared with observed clinical data 2004-2016. While the force of infection is relatively sensitive to the duration of immunity and the number of boosters undertaken, we conclude that periodic large outbreaks of mumps will be sustained for all except the second scenario. This suggests that the current protocol of two vaccinations is optimal in the sense that while there are periodic large outbreaks, the severity of cases in vaccinated individuals is less than in unvaccinated individuals, and the size of the outbreaks does not decrease sufficiently with a third booster to make economic sense. This recommendation relies on continuous efforts to maintain high levels of vaccination uptake.

Keywords: Bio-PEPA; mathematical and computational modeling and simulation; mumps; vaccination; waning immunity.

Figure 1

Confirmed mumps cases, Scotland 1988-2016 and MMR vaccine coverage.

Figure 2

Mumps structure.

Figure 3

Predicted incidence of mumps from 2004 to 2016:: (A) Scenario 1-No vaccination, (B) Scenario 2-Vaccination without waning immunity, (C) Scenario 3-Vaccination with waning immunity, (D) Predicted-Observed data for mumps from 1996 to 2016.

Figure 4

Inter-epidemic period against basic reproductive rate R0 for pre-vaccine era.

Figure 5

Infected against vaccination coverage.

Figure 6

The effect of waning immunity: Left axis: Infected-unvaccinated, Infected-vaccinated. Right axis: natively susceptible and modified susceptible.

Figure 7

Infected against duration of immunity.

Figure 8

Inter-epidemic period against basic reproductive rate R0 for post-vaccine era.