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Abstract
The spread of an epidemic is considered in the context of a SIR spatial
stochastic model that includes a parameter 0≤p≤1 that assigns weights
p and 1−p to global and local infective contacts respectively. For diseases
with low values of the basic reproductive ratio, R0, the value of p turns
out to have a decisive influence on the existence or not of a major outbreak. A
deterministic approximation of the stochastic model, developed by the authors
in previous work, is considered. The existence of a threshold value of p for
exponential epidemic spread is checked in this deterministic context. An
analytical expression, that defines a function of the quotient between the
transmission and recovery rates, is obtained to approximate this threshold.
Different analyses based on intensive stochastic simulations show that this
expression is also a good estimate for a similar threshold value of p in the
stochastic model. In this way, for p values lower than the proposed one, the
probability of a major outbreak becomes negligible even when R0 remains
above 1. The obtained results turn out to be relevant for infectious diseases
with low R0 but high mortality rates such as Ebola or H1N1 influenza. This
study highlights the importance of control measures that minimize the
possibility of global contacts, warning that a small reduction of them could
produce a drastic reduction in the probability of huge outbreaks.
Background Large Phase III trials across Asia and Latin America have recently demonstrated the efficacy of a recombinant, live-attenuated dengue vaccine (Dengvaxia) over the first 25 mo following vaccination. Subsequent data collected in the longer-term follow-up phase, however, have raised concerns about a potential increase in hospitalization risk of subsequent dengue infections, in particular among young, dengue-naïve vaccinees. We here report predictions from eight independent modelling groups on the long-term safety, public health impact, and cost-effectiveness of routine vaccination with Dengvaxia in a range of transmission settings, as characterised by seroprevalence levels among 9-y-olds (SP9). These predictions were conducted for the World Health Organization to inform their recommendations on optimal use of this vaccine. Methods and Findings The models adopted, with small variations, a parsimonious vaccine mode of action that was able to reproduce quantitative features of the observed trial data. The adopted mode of action assumed that vaccination, similarly to natural infection, induces transient, heterologous protection and, further, establishes a long-lasting immunogenic memory, which determines disease severity of subsequent infections. The default vaccination policy considered was routine vaccination of 9-y-old children in a three-dose schedule at 80% coverage. The outcomes examined were the impact of vaccination on infections, symptomatic dengue, hospitalised dengue, deaths, and cost-effectiveness over a 30-y postvaccination period. Case definitions were chosen in accordance with the Phase III trials. All models predicted that in settings with moderate to high dengue endemicity (SP9 ≥ 50%), the default vaccination policy would reduce the burden of dengue disease for the population by 6%–25% (all simulations: –3%–34%) and in high-transmission settings (SP9 ≥ 70%) by 13%–25% (all simulations: 10%– 34%). These endemicity levels are representative of the participating sites in both Phase III trials. In contrast, in settings with low transmission intensity (SP9 ≤ 30%), the models predicted that vaccination could lead to a substantial increase in hospitalisation because of dengue. Modelling reduced vaccine coverage or the addition of catch-up campaigns showed that the impact of vaccination scaled approximately linearly with the number of people vaccinated. In assessing the optimal age of vaccination, we found that targeting older children could increase the net benefit of vaccination in settings with moderate transmission intensity (SP9 = 50%). Overall, vaccination was predicted to be potentially cost-effective in most endemic settings if priced competitively. The results are based on the assumption that the vaccine acts similarly to natural infection. This assumption is consistent with the available trial results but cannot be directly validated in the absence of additional data. Furthermore, uncertainties remain regarding the level of protection provided against disease versus infection and the rate at which vaccine-induced protection declines. Conclusions Dengvaxia has the potential to reduce the burden of dengue disease in areas of moderate to high dengue endemicity. However, the potential risks of vaccination in areas with limited exposure to dengue as well as the local costs and benefits of routine vaccination are important considerations for the inclusion of Dengvaxia into existing immunisation programmes. These results were important inputs into WHO global policy for use of this licensed dengue vaccine.
Highlights • Spatial models will become more important as geolocated data become the norm for infectious disease. • Network models can be thought of as a unifying framework within which metapopulation models and individual-based models are contained. • Work is needed on threshold parameters for spatial models, partly because they often do not produce exponential growth. • Accurately predicting the impact of interventions requires models to be constructed with the appropriate resolution.
