Forecasting Epidemiological Consequences of Maternal Immunization

Background. The increase in the incidence of whooping cough (pertussis) in many countries with high vaccination coverage is alarming. Maternal pertussis immunization has been proposed as an effective means of protecting newborns during the interval between birth and the first routine dose. However, there are concerns regarding potential interference between maternal antibodies and the immune response elicited by the routine schedule, with possible long-term population-level effects. Methods. We formulated a transmission model comprising both primary routine and maternal immunization. This model was examined to evaluate the long-term epidemiological effects of routine and maternal immunization, together with consequences of potential immune interference scenarios. Results. Overall, our model demonstrates that maternal immunization is an effective strategy in reducing the incidence of pertussis in neonates prior to the onset of the primary schedule. However, if maternal antibodies lead to blunting, incidence increases among older age groups. For instance, our model predicts that with 60% routine and maternal immunization coverage and 30% blunting, the incidence among neonates (0–2 months) is reduced by 43%. Under the same scenario, we observe a 20% increase in incidence among children aged 5–10 years. However, the downstream increase in the older age groups occurs with a delay of approximately a decade or more. Conclusions. Maternal immunization has clear positive effects on infant burden of disease, lowering mean infant incidence. However, if maternally derived antibodies adversely affect the immunogenicity of the routine schedule, we predict eventual population-level repercussions that may lead to an overall increase in incidence in older age groups.

To model the effect of the maternal vaccination, a fraction of the newborns (age class 1) start off in the Mv compartment. To model the effect of routine vaccination, a fraction of the individuals either from S or Mv are moved to V on aging from 1 to 2 months of age.
The model is described by the system of differential equations below and was integrated numerically.

Bento et al. Supplementary file
For newborns 2 month old (i=2): For individuals 7 mos to 45+ years (i = 7, . . . , 18) Here ν is the birth rate (constant), µ is the death rate, α is aging, is the waning rate from routine vaccination M is the waning rate from maternal immunization, γ is the recovery rate, ρ is The force of infection in age group i = 1, . . . , 18 is defined as here, q is the probability of infection given exposure in each age group. We fixed the q parameter so R 0 was in agreement with previous pertussis models [13].

S1.4 Calculating Mean age of infection
In the presence of vaccination interventions, mean age of infection (A) is dependent on the effective reproductive number (R p ) [6]. We expect mean age of infection to decrease as R p increases. In our age structured model, we defined mean age of infection as: where, I is the number of infected at each age class, N is the total number of individuals in the population and t age is the time spent in each age class.

Maternal immunization effects on infant cases in a scenario where there is no interference with immune response to routine vaccination
In the absence of interference effects (figure S2), unsurprisingly, as we increase maternal immunization coverage, infant burden is alleviated. This is particularly evident in the first months of life when neonates, in a scenario with no maternal immunization rely on herd immunity to indirectly protect them from coming into contact with infected individuals.

Infected individuals in each age class per 100,000
Maternal Vaccination  Figure S3 illustrates the potential effects of increasing interference of maternal immunization on routine vaccination. As in figure 3, at 60% routine vaccination, with increasing maternal vaccination coverage and low level of blunting (10% primary vaccine failure) we see a decrease in susceptibles in the younger age classes. We also see an increase in susceptibility in older age classes. As blunting increases, there is an increase in susceptibles, specifically in the 3 months to 5 years age classes. At 98% routine vaccination coverage, as the maternal vaccination coverage increases, the potential effects of blunting become more striking in all age classes, with an increase in susceptibles in all age classes except in the neonates. When comparing between routine vaccination coverage levels, at higher coverage, nor surprisingly, susceptibility decreases, with blunting effects being more pronounced especially in the younger age classes, due to the increased transmission.

Mat vac 30%
Mat vac 60%   Figure S4 illustrates that our modeling results anticipate a downstream risk associated with MatAbs interference, namely an eventual increase in prevalence among older age groups. Simulations indicate these effects may take a decade or more to be made manifest. We show that the magnitude of these repercussions at the population level is dependent on the severity of MatAbs interference.

S2.2 Elasticity analysis
By allowing both maternal immunization and blunting (the measure of interference of maternally derived immunity on immune response to routine vaccination) to vary by small amounts, we measured the relative response of those "perturbations", in a deterministic way, on both mean age of infection and mean infant incidence (0-3 mo

Mean age of infection increase
Mean age of infection decrease

No change
Mean age of infection 14 16 18 Figure S5. Mean age of infection. Effects of small changes in blunting levels (primary vaccine failure) and maternal immunization, at a 60% routine vaccination coverage. In pale yellow is the baseline level and in red and blue are the effects of those small changes on mean age of infection. S11

Mean infant incidence
The results from our elasticity analyses show that, at 60% routine vaccination coverage, not surprisingly, infant incidence decreases with increase of maternal immunization coverage ( Figure   S6). We compare the effects of small changes in blunting and maternal immunization on mean age at infection. At lower maternal vaccination coverage, the effects of increasing blunting are almost negligible. Mean infant incidence is more sensitive to changes in blunting at higher levels of maternal immunization coverage. Mean infant incidence decreases as maternal immunization coverage increases.Incidence is mostly affected by maternal immunization coverage (row comparisons).
Blunting levels changes have a reduced effect on incidence (column comparison), but those effects are less noticeable at lower levels of maternal immunization coverage.

Mean infant incidence
Mean infant incidence decrease

Mean age of infection increase
Mean age of infection decrease

Mean infant incidence
The results from our elasticity analyses show that, at 98% routine vaccination coverage, not surprisingly, infant incidence decreases with increase of maternal immunization coverage ( Figure S8).
Mean infant incidence decreases in comparison with the 60% routine vaccination coverage.like with the 60% routine coverage scenario, incidence is mostly affected by maternal immunization coverage (row comparisons). Blunting levels changes have a reduced effect on incidence (column comparison ( Figures S6 and S8), but those effects are less noticeable at lower levels of maternal immunization coverage. We compare the effects of small changes in blunting and maternal immunization on mean age at infection. At lower maternal vaccination coverage, the effects of increasing blunting are almost negligible. Mean infant incidence is more sensitive to changes in blunting at higher levels of maternal immunization coverage. Mean infant incidence decreases as maternal immunization coverage increases. When blunting is low (8-12%), a small decrease in maternal vaccination, results in an increase in incidence. At high levels of maternal vaccination, incidence is very sensitive to changes in blunting levels even when not changing maternal immunization coverage ( Figure S8).

Mean infant incidence
Mean infant incidence increase

Mean infant incidence
Mean infant incidence decrease Figure S8. Mean infant incidence with 98% routine vaccine coverage. Effects of small changes in blunting levels (primary vaccine failure) and maternal immunization, at a 98% routine vaccination coverage. In pale yellow is the baseline level and in red and blue are the effects of those small changes.The size of the bubbles indicate the size of effect and the colour change indicate a decrease (blue) or an increase in mean infant incidence at middle points of combinations of blunting effects and maternal immunization coverage.