Temporal Evolution of Immunity Distributions in a Population with Waning and Boosting

Abstract

We investigate the temporal evolution of the distribution of immunities in a population, which is determined by various epidemiological, immunological, and demographical phenomena: after a disease outbreak, recovered individuals constitute a large immune population; however, their immunity is waning in the long term and they may become susceptible again. Meanwhile, their immunity can be boosted by repeated exposure to the pathogen, which is linked to the density of infected individuals present in the population. This prolongs the length of their immunity. We consider a mathematical model formulated as a coupled system of ordinary and partial differential equations that connects all these processes and systematically compare a number of boosting assumptions proposed in the literature, showing that different boosting mechanisms lead to very different stationary distributions of the immunity at the endemic steady state. In the situation of periodic disease outbreaks, the waveforms of immunity distributions are studied and visualized. Our results show that there is a possibility to infer the boosting mechanism from the population level immune dynamics.

Effects of boosting and waning in highly exposed populations on dengue epidemic dynamics

“…Our model extends from the theoretical model frameworks by Barbarossa et al. ( 33 , 35 , 76 ). Here, we categorized the recovered population into three compartments tracking immunity by titer: R L , from individuals with transient immunity; R M , from individuals with intermediate immunity; and R H , from those with high immunity.…”

“…However, although transient, 43% of the participants had a ≥4-fold rise in antibody titer, demonstrating homotypic boosting (16,17). A few transmission models have explored the role of boosting in general (33) and in protection against symptomatic and severe dengue (16,17). Alexander et al (16) built two-and four-serotype models including immune waning, with and without boosting, and varying cross-protection to explain the fluctuations in the inapparent to symptomatic ratio in DENV infections documented worldwide.…”

“…Here, we draw on concepts from theoretical models (16,33,(35)(36)(37) to build a susceptible-infected-recovered-susceptible (SIRStype) model that tracks immunity by titer rather than number of prior infections to examine the effect of reexposure on dengue epidemic dynamics. Our model was simulated to predict dengue incidence using estimates from the DENV-binding antibody titers measured annually in children and adults in Nicaragua after the Zika pandemic and a major epidemic caused by DENV2, enabling more accurate estimates of boosting.…”

“…However, although transient, 43% of the participants had a ≥4-fold rise in antibody titer, demonstrating homotypic boosting ( 16 , 17 ). A few transmission models have explored the role of boosting in general ( 33 ) and in protection against symptomatic and severe dengue ( 16 , 17 ). Alexander et al.…”

Comparative reconstruction of SARS-CoV-2 transmission in three African countries using a mathematical model integrating immunity data

“…We compared the SARS-CoV-2 pandemic dynamics in Senegal, Madagascar, and Tunisia using the susceptible–exposed–infected–recovered/Death (SEIR)/DS model developed by White and Medley [7] and reviewed by Barbarossa et al. [8] ( Figure 1 ). The susceptible compartment ( S ) was divided into two groups: S 1 for individuals who had previously been infected, identified by antibodies (Abs) to S/RBD but not to N, and S 2 for those without prior infection (no N and no S/RBD).…”