A mathematical model for distributed waning of vaccine-derived immunity: Characterizing dynamical impact on measles elimination

Abstract

The worldwide resurgence of measles outbreaks, particularly in western nations, has become a serious global health concern. Often, it fails to meet the regional measles elimination goals proposed by the World Health Organization (WHO). Several clinical studies pointed out that antibodies induced by the Measles–Mumps–Rubella vaccine wane over time, resulting in drops in the Herd-Immunity level despite maintaining high vaccine coverage in the population. To portray this nonlinear interaction between the waning of vaccine-induced immunity and disease transmission, we develop a measles model with a distributed delay that takes into account varying immunity periods in the population. We use different probability distributions to characterize distributed delay. Comparing scenarios under different types of distributions, we compute and show how it affects the control reproduction number, indicating when measles elimination is not possible under a simple routine immunization program. We determine critical vaccination coverage for different types of waning distribution. Our work illustrates that a supplementary immunization campaign in addition to routine vaccination is essential to control the outbreak and achieve elimination goals.

Keywords

• Delay model
• Waning immunity
• Measles elimination
• MMR vaccine