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Hannah C. Slater, Amanda Ross, André Lin Ouédraogo, Lisa J. White, Chea Nguon, Patrick G.T. Walker, Pengby Ngor, Ricardo Aguas, Sheetal P. Silal, Arjen M. Dondorp, Paul La Barre, Robert Burton, Robert W. Sauerwein, Chris Drakeley, Thomas A. Smith, Teun Bousema, Azra C. Ghani


Mass-screen-and-treat and targeted mass-drug-administration strategies are being considered as a means to interrupt transmission of Plasmodium falciparum malaria. However, the effectiveness of such strategies will depend on the extent to which current and future diagnostics are able to detect those individuals who are infectious to mosquitoes. We estimate the relationship between parasite density and onward infectivity using sensitive quantitative parasite diagnostics and mosquito feeding assays from Burkina Faso. We find that a diagnostic with a lower detection limit of 200 parasites per microlitre would detect 55% of the infectious reservoir (the combined infectivity to mosquitoes of the whole population weighted by how often each individual is bitten) whereas a test with a limit of 20 parasites per microlitre would detect 83% and 2 parasites per microlitre would detect 95% of the infectious reservoir. Using mathematical models, we show that increasing the diagnostic sensitivity from 200 parasites per microlitre (equivalent to microscopy or current rapid diagnostic tests) to 2 parasites per microlitre would increase the number of regions where transmission could be interrupted with a mass-screen-and-treat programme from an entomological inoculation rate below 1 to one of up to 4. The higher sensitivity diagnostic could reduce the number of treatment rounds required to interrupt transmission in areas of lower prevalence. We predict that mass-screen-and-treat with a highly sensitive diagnostic is less effective than mass drug administration owing to the prophylactic protection provided to uninfected individuals by the latter approach. In low-transmission settings such as those in Southeast Asia, we find that a diagnostic tool with a sensitivity of 20 parasites per microlitre may be sufficient for targeted mass drug administration because this diagnostic is predicted to identify a similar village population prevalence compared with that currently detected using polymerase chain reaction if treatment levels are high and screening is conducted during the dry season. Along with other factors, such as coverage, choice of drug, timing of the intervention, importation of infections, and seasonality, the sensitivity of the diagnostic can play a part in increasing the chance of interrupting transmission.


A novel method is presented to compute the exit time for the stochastic simulation algorithm. The method is based on the addition of a series of random variables and is derived using the convolution theorem. The final distribution is derived and approximated in the frequency domain. The distribution for the final time is transformed back to the real domain and can be sampled from in a simulation. The result is an approximation of the classical stochastic simulation algorithm that requires fewer random variates. An analysis of the error and speedup compared to the stochastic simulation algorithm is presented.

Dr Melissa A Penny, PhD, Robert Verity, PhD, Caitlin A Bever, PhD, Christophe Sauboin, MA, Katya Galactionova, MA, Stefan Flasche, PhD, Michael T White, PhD, Edward A Wenger, PhD, Nicolas Van de Velde, PhD, Peter Pemberton-Ross, PhD, Jamie T Griffin, PhD, Prof Thomas A Smith, PhD, Philip A Eckhoff, PhD, Farzana Muhib, MPH, Mark Jit, PhD, Prof Azra C Ghani, PhD



The phase 3 trial of the RTS,S/AS01 malaria vaccine candidate showed modest efficacy of the vaccine against Plasmodium falciparum malaria, but was not powered to assess mortality endpoints. Impact projections and cost-effectiveness estimates for longer timeframes than the trial follow-up and across a range of settings are needed to inform policy recommendations. We aimed to assess the public health impact and cost-effectiveness of routine use of the RTS,S/AS01 vaccine in African settings.


We compared four malaria transmission models and their predictions to assess vaccine cost-effectiveness and impact. We used trial data for follow-up of 32 months or longer to parameterise vaccine protection in the group aged 5–17 months. Estimates of cases, deaths, and disability-adjusted life-years (DALYs) averted were calculated over a 15 year time horizon for a range of levels of Plasmodium falciparum parasite prevalence in 2–10 year olds (PfPR2–10; range 3–65%). We considered two vaccine schedules: three doses at ages 6, 7·5, and 9 months (three-dose schedule, 90% coverage) and including a fourth dose at age 27 months (four-dose schedule, 72% coverage). We estimated cost-effectiveness in the presence of existing malaria interventions for vaccine prices of US$2–10 per dose.


In regions with a PfPR2–10 of 10–65%, RTS,S/AS01 is predicted to avert a median of 93 940 (range 20 490–126 540) clinical cases and 394 (127–708) deaths for the three-dose schedule, or 116 480 (31 450–160 410) clinical cases and 484 (189–859) deaths for the four-dose schedule, per 100 000 fully vaccinated children. A positive impact is also predicted at a PfPR2–10 of 5–10%, but there is little impact at a prevalence of lower than 3%. At $5 per dose and a PfPR2–10 of 10–65%, we estimated a median incremental cost-effectiveness ratio compared with current interventions of $30 (range 18–211) per clinical case averted and $80 (44–279) per DALY averted for the three-dose schedule, and of $25 (16–222) and $87 (48–244), respectively, for the four-dose schedule. Higher ICERs were estimated at low PfPR2–10 levels.


We predict a significant public health impact and high cost-effectiveness of the RTS,S/AS01 vaccine across a wide range of settings. Decisions about implementation will need to consider levels of malaria burden, the cost-effectiveness and coverage of other malaria interventions, health priorities, financing, and the capacity of the health system to deliver the vaccine.


PATH Malaria Vaccine Initiative; Bill & Melinda Gates Foundation; Global Good Fund; Medical Research Council; UK Department for International Development; GAVI, the Vaccine Alliance; WHO.

Alexandra E. Brown, Hiromasa Okayasu, Michael M. Nzioki, Mufti Z. Wadood, Guillaume Chabot-Couture, Arshad Quddus, George Walker and Roland W. Sutter


Monitoring the quality of supplementary immunization activities (SIAs) is a key tool for polio eradication. Regular monitoring data, however, are often unreliable, showing high coverage levels in virtually all areas, including those with ongoing virus circulation. To address this challenge, lot quality assurance sampling (LQAS) was introduced in 2009 as an additional tool to monitor SIA quality. Now used in 8 countries, LQAS provides a number of programmatic benefits: identifying areas of weak coverage quality with statistical reliability, differentiating areas of varying coverage with greater precision, and allowing for trend analysis of campaign quality. LQAS also accommodates changes to survey format, interpretation thresholds, evaluations of sample size, and data collection through mobile phones to improve timeliness of reporting and allow for visualization of campaign quality. LQAS becomes increasingly important to address remaining gaps in SIA quality and help focus resources on high-risk areas to prevent the continued transmission of wild poliovirus.

Benjamin M Althouse, Samuel V Scarpino, Lauren Ancel Meyers, John W Ayers, Marisa Bargsten, Joan Baumbach, John S Brownstein, Lauren Castro, Hannah Clapham, Derek AT Cummings, Sara Del Valle, Stephen Eubank, Geoffrey Fairchild, Lyn Finelli, Nicholas Generous, Dylan George, David R Harper, Laurent Hébert-Dufresne, Michael A Johansson, Kevin Konty, Marc Lipsitch, Gabriel Milinovich, Joseph D Miller, Elaine O Nsoesie, Donald R Olson, Michael Paul, Philip M Polgreen, Reid Priedhorsky, Jonathan M Read, Isabel Rodríguez-Barraquer, Derek J Smith, Christian Stefansen, David L Swerdlow, Deborah Thompson, Alessandro Vespignani and Amy Wesolowski


Novel data streams (NDS), such as web search data or social media updates, hold promise for enhancing the capabilities of public health surveillance. In this paper, we outline a conceptual framework for integrating NDS into current public health surveillance. Our approach focuses on two key questions: What are the opportunities for using NDS and what are the minimal tests of validity and utility that must be applied when using NDS? Identifying these opportunities will necessitate the involvement of public health authorities and an appreciation of the diversity of objectives and scales across agencies at different levels (local, state, national, international). We present the case that clearly articulating surveillance objectives and systematically evaluating NDS and comparing the performance of NDS to existing surveillance data and alternative NDS data is critical and has not sufficiently been addressed in many applications of NDS currently in the literature.

Michael Famulare, Stewart Chang, Jane Iber, Kun Zhao, Johnson A. Adeniji, David Bukbuk, Marycelin Baba, Matthew Behrend, Cara C. Burns and M. Steven Oberste


To assess the dynamics of genetic reversion of live poliovirus vaccine in humans, we studied molecular evolution in Sabin-like poliovirus isolates from Nigerian acute flaccid paralysis cases obtained from routine surveillance. We employed a novel modeling approach to infer substitution and recombination rates from whole-genome sequences and information about poliovirus infection dynamics and individual vaccination history. We confirmed observations from a recent vaccine trial that VP1 substitution rates are increased for Sabin-like isolates relative to the wild-type rate due to increased non-synonymous substitution rates. We also inferred substitution rates for attenuating nucleotides and confirmed that reversion can occur in days to weeks after vaccination. We combine our observations for Sabin-like evolution with the wild-type circulating VP1 molecular clock to infer that the mean time from the initiating vaccine dose to the earliest detection of circulating vaccine-derived poliovirus (cVDPV) is 300 days for type 1, 210 days for type 2, and 390 days for type 3. Phylogenetic relationships indicated transient local transmission of Sabin 3 and possibly Sabin 1 during periods of low wild polio incidence. Comparison of Sabin-like recombinants with known Nigerian VDPV recombinants shows that while recombination with non-Sabin enteroviruses is associated with cVDPV, the recombination rates are similar for Sabin-Sabin and Sabin-non-Sabin enterovirus recombination after accounting for time from dose to detection. Our study provides a comprehensive picture of the evolutionary dynamics of oral polio vaccine in the field.

IMPORTANCE The global polio eradication effort has completed its twenty-sixth year. Despite success in eliminating wild poliovirus from most of the world, polio persists in populations where logistical, social, and political factors have not allowed for vaccination programs of sustained high quality. One issue of critical importance is eliminating circulating vaccine-derived poliovirus (cVDPV) that have properties indistinguishable from wild poliovirus and can cause paralytic disease. cVDPV emerges due to the genetic instability of the Sabin viruses used in oral polio vaccine (OPV) in populations that have low immunity to poliovirus. However, the dynamics responsible are incompletely understood because it has historically been difficult to gather and interpret data about OPV evolution in regions where cVDPV has occurred. This study is the first to combine whole-genome sequencing of poliovirus isolates collected during routine surveillance with knowledge about polio intra-host dynamics to provide quantitative insight into polio vaccine evolution in the field.


In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to a subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves observable functions on the state-space of a dynamical system. Dominant terms in the Koopman expansion are typically computed using dynamic mode decomposition (DMD). DMD uses linear observations of the state variables, and it has recently been shown that this may be too restrictive for nonlinear systems. It remains an open challenge how to choose the right nonlinear observable functions to form a subspace where it is possible to obtain efficient linear reduced-order models.

Here, we investigate the choice of observable functions for Koopman analysis. First, we note that in order to obtain a linear Koopman system that advances the original states, it is helpful to include these states in the observable subspace, as in DMD. We then categorize dynamical systems by whether or not there exists a Koopman-invariant observable subspace that includes the state variables as observables. In particular, we note that this is only possible when there is a single isolated fixed point, as systems with multiple fixed points or more complicated attractors are not topologically conjugate to a finite-dimensional linear system; this is illustrated using the logistic map. Second, we present a data-driven strategy to identify the relevant observable functions for Koopman analysis. We leverage a new algorithm that determines relevant terms in a dynamical system by 1 regularized regression of the data in a nonlinear function space; we also show how this algorithm is related to DMD. Finally, we demonstrate the usefulness of nonlinear observable subspaces in the design of Koopman operator optimal control laws for fully nonlinear systems using techniques from linear optimal control.

Dr Jeffrey W Eaton, Nicolas Bacaër, PhD, Anna Bershteyn, PhD, Valentina Cambiano, PhD, Anne Cori, PhD, Prof Rob E Dorrington, MPhil, Prof Christophe Fraser, PhD, Chaitra Gopalappa, PhD, Jan A C Hontelez, PhD, Leigh F Johnson, PhD, Daniel J Klein, PhD, Prof Andrew N Phillips, PhD, Carel Pretorius, PhD, John Stover, MA, Prof Thomas M Rehle, MD, Prof Timothy B Hallett, PhD



Mathematical models are widely used to simulate the effects of interventions to control HIV and to project future epidemiological trends and resource needs. We aimed to validate past model projections against data from a large household survey done in South Africa in 2012.


We compared ten model projections of HIV prevalence, HIV incidence, and antiretroviral therapy (ART) coverage for South Africa with estimates from national household survey data from 2012. Model projections for 2012 were made before the publication of the 2012 household survey. We compared adult (age 15–49 years) HIV prevalence in 2012, the change in prevalence between 2008 and 2012, and prevalence, incidence, and ART coverage by sex and by age groups between model projections and the 2012 household survey.


All models projected lower prevalence estimates for 2012 than the survey estimate (18·8%), with eight models' central projections being below the survey 95% CI (17·5–20·3). Eight models projected that HIV prevalence would remain unchanged (n=5) or decline (n=3) between 2008 and 2012, whereas prevalence estimates from the household surveys increased from 16·9% in 2008 to 18·8% in 2012 (difference 1·9, 95% CI −0·1 to 3·9). Model projections accurately predicted the 1·6 percentage point prevalence decline (95% CI −0·3 to 3·5) in young adults aged 15–24 years, and the 2·2 percentage point (0·5 to 3·9) increase in those aged 50 years and older. Models accurately represented the number of adults on ART in 2012; six of ten models were within the survey 95% CI of 1·54–2·12 million. However, the differential ART coverage between women and men was not fully captured; all model projections of the sex ratio of women to men on ART were lower than the survey estimate of 2·22 (95% CI 1·73–2·71).


Projections for overall declines in HIV epidemics during the ART era might have been optimistic. Future treatment and HIV prevention needs might be greater than previously forecasted. Additional data about service provision for HIV care could help inform more accurate projections.


Bill & Melinda Gates Foundation.

S. Bhatt, D.J. Weiss, E. Cameron, D. Bisanzio, B. Mappin, U. Dalrymple, K. E. Battle, C. L. Moyes, A. Henry, P. A. Eckhoff, E. A. Wenger, O. Briët, M. A. Penny, T. A. Smith, A. Bennett, J. Yukich, T. P. Eisele, J. T. Griffin, C. A. Fergus, M. Lynch, F. Lindgren, J. M. Cohen, C. L. J. Murray, D. L. Smith, S. I. Hay, R. E. Cibulskis & P. W. Gething


Since the year 2000, a concerted campaign against malaria has led to unprecedented levels of intervention coverage across sub-Saharan Africa. Understanding the effect of this control effort is vital to inform future control planning. However, the effect of malaria interventions across the varied epidemiological settings of Africa remains poorly understood owing to the absence of reliable surveillance data and the simplistic approaches underlying current disease estimates. Here we link a large database of malaria field surveys with detailed reconstructions of changing intervention coverage to directly evaluate trends from 2000 to 2015, and quantify the attributable effect of malaria disease control efforts. We found that Plasmodium falciparum infection prevalence in endemic Africa halved and the incidence of clinical disease fell by 40% between 2000 and 2015. We estimate that interventions have averted 663 (542–753 credible interval) million clinical cases since 2000. Insecticide-treated nets, the most widespread intervention, were by far the largest contributor (68% of cases averted). Although still below target levels, current malaria interventions have substantially reduced malaria disease incidence across the continent. Increasing access to these interventions, and maintaining their effectiveness in the face of insecticide and drug resistance, should form a cornerstone of post-2015 control strategies.


The ability to discover physical laws and governing equations from data is one of humankind’s greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development of knowledge and enabled advanced technological achievements, including aircraft, combustion engines, satellites, and electrical power. In this work, we combine sparsity-promoting techniques and machine learning with nonlinear dynamical systems to discover governing physical equations from measurement data. The only assumption about the structure of the model is that there are only a few important terms that govern the dynamics, so that the equations are sparse in the space of possible functions; this assumption holds for many physical systems. In particular, we use sparse regression to determine the fewest terms in the dynamic governing equations required to accurately represent the data. The resulting models are parsimonious, balancing model complexity with descriptive ability while avoiding overfitting. We demonstrate the algorithm on a wide range of problems, from simple canonical systems, including linear and nonlinear oscillators and the chaotic Lorenz system, to the fluid vortex shedding behind an obstacle. The fluid example illustrates the ability of this method to discover the underlying dynamics of a system that took experts in the community nearly 30 years to resolve. We also show that this method generalizes to parameterized, time-varying, or externally forced systems.