Implications of vaccination and waning immunity

Heffernan, Jane M.; Keeling, Matthew James

doi:10.1098/rspb.2009.0057

Cited by 95 publications

(102 citation statements)

References 52 publications

(62 reference statements)

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“…Transient dynamics such as the honeymoon period and outbreaks after the start of vaccination (illustrated in Figure 3.2) can be affected by the distribution of the waning period. Heffernan and Keeling [7] demonstrated that an SEIR model with both waning, boosting of immunity and multiple disease compartments may generate sustained cycles of disease outbreaks. They noted that these cycles are not maintained when assuming exponential waning time.…”

Section: Discussionmentioning

confidence: 99%

Epidemiological Consequences of Imperfect Vaccines for Immunizing Infections

Magpantay¹,

Riolo²,

Cellès³

et al. 2014

SIAM J. Appl. Math.

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The control of some childhood diseases has proven to be difficult even in countries that maintain high vaccination coverage. This may be due to the use of imperfect vaccines and there has been much discussion on the different modes by which vaccines might fail. To understand the epidemiological implications of some of these different modes, we performed a systematic analysis of a model based on the standard SIR equations with a vaccinated component that permits vaccine failure in degree (“leakiness”), take (“all-or-nothingness”) and duration (waning of vaccine-derived immunity). The model was first considered as a system of ordinary differential equations, then extended to a system of partial differential equations to accommodate age structure. We derived analytic expressions for the steady states of the system and the final age distributions in the case of homogenous contact rates. The stability of these equilibria are determined by a threshold parameter Rp, a function of the vaccine failure parameters and the coverage p. The value of p for which Rp = 1 yields the critical vaccination ratio, a measure of herd immunity. Using this concept we can compare vaccines that confer the same level of herd immunity to the population but may fail at the individual level in different ways. For any fixed Rp > 1, the leaky model results in the highest prevalence of infection, while the all-or-nothing and waning models have the same steady state prevalence. The actual composition of a vaccine cannot be determined on the basis of steady state levels alone, however the distinctions can be made by looking at transient dynamics (such as after the onset of vaccination), the mean age of infection, the age distributions at steady state of the infected class, and the effect of age-specific contact rates.

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Section: Discussionmentioning

confidence: 99%

Epidemiological Consequences of Imperfect Vaccines for Immunizing Infections

Magpantay¹,

Riolo²,

Cellès³

et al. 2014

SIAM J. Appl. Math.

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show abstract

“…Seasonality in the SIR model tends to drive regular multi-annual epidemic disease outbreaks as is seen in childhood infections such as measles [21 -23]. Vaccination has also been modelled as removal of individuals from the susceptible class directly to the immune class without an infectious stage and at a rate independent of pathogen density in the population [24,25]. However, these classic SIR-type models do not capture the population dynamics with immune priming, where a proportion of individuals do not become infectious but are primed following pathogen exposure and have reduced risk of becoming infectious on subsequent exposure.…”

Section: Introductionmentioning

confidence: 99%

The epidemiological consequences of immune priming

2012

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Exposure to low doses of pathogens that do not result in the host becoming infectious may 'prime' the immune response and increase protection to subsequent challenge. There is increasing evidence that such immune priming is a widespread and important feature of invertebrate host-pathogen interactions. Immune priming clearly has implications for individual hosts but will also have population-level implications. We present a susceptible-primed-infectious model-in contrast to the classic susceptibleinfectious-recovered framework-to investigate the impacts of immune priming on pathogen persistence and population stability. We describe impacts of immune priming on the epidemiology of the disease in both constant and seasonal environments. A key result is that immune priming may act to destabilize population dynamics. In particular, when the proportion of individuals becoming primed rather than infected is high, but this priming does not confer full immunity, the population may be strongly destabilized through the generation of limit cycles. We discuss the implications of our model both in the context of invertebrate immunity and more widely.

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“…Such a simplifying assumption is often used to model childhood vaccination that occurs at a very young age [5,8–11], before children reach ages that are associated with higher contact rates such as when they start going to school or daycare.…”

Section: Homogeneous Modelmentioning

confidence: 99%

Vaccine impact in homogeneous and age-structured models

Magpantay

2017

J. Math. Biol.

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A general model of an imperfect vaccine for a childhood disease is presented and the effects of different types of vaccine failure on transmission were investigated using models that consider both homogeneous and age-specific mixing. The models are extensions of the standard SEIR equations with an additional vaccinated component that allows for five different vaccine parameters: three types of vaccine failure in decreasing susceptibility to infection via failure in degree (“leakiness”), take (“all-or-nothingness”) and duration (waning of vaccine-derived immunity); one parameter reflecting the relative reduction in infectiousness of vaccinated individuals who get infected; and one parameter that reflects the relative reduction in reporting probability of vaccinated individuals due to a possible reduction in severity of symptoms. Only the first four parameters affect disease transmission (as measured by the basic reproduction number). The reduction in transmission due to vaccination is different for age-structured models than for homogeneous models. Notably, if the vaccine exhibits waning protection this could be larger for an age-structured model with high contact rates between young children who are still protected by the vaccine and lower contact rates between adults for whom protection might have already waned. Analytic expressions for age-specific “vaccine impacts” were also derived. The overall vaccine impact is bounded between the age-specific impact for the oldest age class and that of the youngest age class.

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Implications of vaccination and waning immunity

Cited by 95 publications

References 52 publications

Epidemiological Consequences of Imperfect Vaccines for Immunizing Infections

Epidemiological Consequences of Imperfect Vaccines for Immunizing Infections

The epidemiological consequences of immune priming

Vaccine impact in homogeneous and age-structured models

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