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The renewed effort to eliminate malaria and permanently remove its tremendous burden highlights questions of what combination of tools would be sufficient in various settings and what new tools need to be developed. Gene drive mosquitoes constitute a promising set of tools, with multiple different possible approaches including population replacement with introduced genes limiting malaria transmission, driving-Y chromosomes to collapse a mosquito population, and gene drive disrupting a fertility gene and thereby achieving population suppression or collapse. Each of these approaches has had recent success and advances under laboratory conditions, raising the urgency for understanding how each could be deployed in the real world and the potential impacts of each. New analyses are needed as existing models of gene drive primarily focus on nonseasonal or nonspatial dynamics. We use a mechanistic, spatially explicit, stochastic, individual-based mathematical model to simulate each gene drive approach in a variety of sub-Saharan African settings. Each approach exhibits a broad region of gene construct parameter space with successful elimination of malaria transmission due to the targeted vector species. The introduction of realistic seasonality in vector population dynamics facilitates gene drive success compared with nonseasonal analyses. Spatial simulations illustrate constraints on release timing, frequency, and spatial density in the most challenging settings for construct success. Within its parameter space for success, each gene drive approach provides a tool for malaria elimination unlike anything presently available. Provided potential barriers to success are surmounted, each achieves high efficacy at reducing transmission potential and lower delivery requirements in logistically challenged settings.


Identifying governing equations from data is a critical step in the modeling and control of complex dynamical systems. Here, we investigate the data-driven identification of nonlinear dynamical systems with inputs and forcing using regression methods, including sparse regression. Specifically, we generalize the sparse identification of nonlinear dynamics (SINDY) algorithm to include external inputs and feedback control. This method is demonstrated on examples including the Lotka-Volterra predator-prey model and the Lorenz system with forcing and control. We also connect the present algorithm with the dynamic mode decomposition (DMD) and Koopman operator theory to provide a broader context.


This work develops compressed sensing strategies for computing the dynamic mode decomposition (DMD) from heavily subsampled or compressed data. The resulting DMD eigenvalues are equal to DMD eigenvalues from the full-state data. It is then possible to reconstruct full-state DMD eigenvectors using  1-minimization or greedy algorithms. If full-state snapshots are available, it may be computationally beneficial to compress the data, compute DMD on the compressed data, and then reconstruct full-state modes by applying the compressed DMD transforms to full-state snapshots.

 These results rely on a number of theoretical advances. First, we establish connections between DMD on full-state and compressed data. Next, we demonstrate the invariance of the DMD algorithm to left and right unitary transformations. When data and modes are sparse in some transform basis, we show a similar invariance of DMD to measurement matrices that satisfy the restricted isometry property from compressed sensing. We demonstrate the success of this architecture on two model systems. In the first example, we construct a spatial signal from a sparse vector of Fourier coefficients with a linear dynamical system driving the coefficients. In the second example, we consider the double gyre flow field, which is a model for chaotic mixing in the ocean. 

Fig. 3

Flow-chart illustrating compressed DMD and compressed sensing DMD.


Despite the increasing availability of high performance computing capabilities, analysis and characterization of stochastic biochemical systems remain a computational challenge. To address this challenge, the Stochastic Parameter Search for Events (SParSE) was developed to automatically identify reaction rates that yield a probabilistic user-specified event. SParSE consists of three main components: the multi-level cross-entropy method, which identifies biasing parameters to push the system toward the event of interest, the related inverse biasing method, and an optional interpolation of identified parameters. While effective for many examples, SParSE depends on the existence of a sufficient amount of intrinsic stochasticity in the system of interest. In the absence of this stochasticity, SParSE can either converge slowly or not at all.

We have developed SParSE++, a substantially improved algorithm for characterizing target events in terms of system parameters. SParSE++ makes use of a series of novel parameter leaping methods that accelerate the convergence rate to the target event, particularly in low stochasticity cases. In addition, the interpolation stage is modified to compute multiple interpolants and to choose the optimal one in a statistically rigorous manner. We demonstrate the performance of SParSE++ on four example systems: a birth-death process, a reversible isomerization model, SIRS disease dynamics, and a yeast polarization model. In all four cases, SParSE++ shows significantly improved computational efficiency over SParSE, with the largest improvements resulting from analyses with the strictest error tolerances.

As researchers continue to model realistic biochemical systems, the need for efficient methods to characterize target events will grow. The algorithmic advancements provided by SParSE++ fulfill this need, enabling characterization of computationally intensive biochemical events that are currently resistant to analysis.

Milen Nikolov, PhD, Caitlin A. Bever, PhD, Alexander Upfill-Brown, Busiku Hamainza, John M. Miller, Philip A. Eckhoff, PhD, Edward A. Wenger, PhD, Jaline Gerardin, PhD


As more regions approach malaria elimination, understanding how different interventions interact to reduce transmission becomes critical. The Lake Kariba area of Southern Province, Zambia, is part of a multi-country elimination effort and presents a particular challenge as it is an interconnected region of variable transmission intensities. In 2012–13, six rounds of mass test-and-treat drug campaigns were carried out in the Lake Kariba region. A spatial dynamical model of malaria transmission in the Lake Kariba area, with transmission and climate modeled at the village scale, was calibrated to the 2012–13 prevalence survey data, with case management rates, insecticide-treated net usage, and drug campaign coverage informed by surveillance. The model captured the spatio-temporal trends of decline and rebound in malaria prevalence in 2012–13 at the village scale. Various interventions implemented between 2016–22 were simulated to compare their effects on reducing regional transmission and achieving and maintaining elimination through 2030. Simulations predict that elimination requires sustaining high coverage with vector control over several years. When vector control measures are well-implemented, targeted mass drug campaigns in high-burden areas further increase the likelihood of elimination, although drug campaigns cannot compensate for insufficient vector control. If infections are regularly imported from outside the region into highly receptive areas, vector control must be maintained within the region until importations cease. Elimination in the Lake Kariba region is possible, although human movement both within and from outside the region risk damaging the success of elimination programs.


The increasing ubiquity of complex systems that require control is a challenge for existing methodologies in characterization and controller design when the system is high-dimensional, nonlinear, and without physics-based governing equations. We review standard model reduction techniques such as Proper Orthogonal Decomposition (POD) with Galerkin projection and Balanced POD (BPOD). Further, we discuss the link between these equation-based methods and recently developed equation-free methods such as the Dynamic Mode Decomposition and Koopman operator theory. These data-driven methods can mitigate the challenge of not having a well-characterized set of governing equations. We illustrate that this equation-free approach that is being applied to measurement data from complex systems can be extended to include inputs and control. Three specific research examples are presented that extend current equation-free architectures toward the characterization and control of complex systems. These examples motivate a potentially revolutionary shift in the characterization of complex systems and subsequent design of objective-based controllers for data-driven models.

Andrew M. Bellinger, Mousa Jafari, Tyler M. Grant, Shiyi Zhang, Hannah C. Slater, Edward A. Wenger, Stacy Mo, Young-Ah Lucy Lee, Hormoz Mazdiyasni, Lawrence Kogan, Ross Barman, Cody Cleveland, Lucas Booth, Taylor Bensel, Daniel Minahan, Haley M. Hurowitz, Tammy Tai, Johanna Daily, Boris Nikolic, Lowell Wood, Philip A. Eckhoff, Robert Langer, and Giovanni Traverso


Efforts at elimination of scourges, such as malaria, are limited by the logistic challenges of reaching large rural populations and ensuring patient adherence to adequate pharmacologic treatment. We have developed an oral, ultra–long-acting capsule that dissolves in the stomach and deploys a star-shaped dosage form that releases drug while assuming a geometry that prevents passage through the pylorus yet allows passage of food, enabling prolonged gastric residence. This gastric-resident, drug delivery dosage form releases small-molecule drugs for days to weeks and potentially longer. Upon dissolution of the macrostructure, the components can safely pass through the gastrointestinal tract. Clinical, radiographic, and endoscopic evaluation of a swine large-animal model that received these dosage forms showed no evidence of gastrointestinal obstruction or mucosal injury. We generated long-acting formulations for controlled release of ivermectin, a drug that targets malaria-transmitting mosquitoes, in the gastric environment and incorporated these into our dosage form, which then delivered a sustained therapeutic dose of ivermectin for up to 14 days in our swine model. Further, by using mathematical models of malaria transmission that incorporate the lethal effect of ivermectin against malaria-transmitting mosquitoes, we demonstrated that this system will boost the efficacy of mass drug administration toward malaria elimination goals. Encapsulated, gastric-resident dosage forms for ultra–long-acting drug delivery have the potential to revolutionize treatment options for malaria and other diseases that affect large populations around the globe for which treatment adherence is essential for efficacy.

Prof Nicolas A Menzies, PhD, Gabriela B Gomez, PhD, Fiammetta Bozzani, MSc, Susmita Chatterjee, PhD, Nicola Foster, MPH, Ines Garcia Baena, MSc, Yoko V Laurence, MSc, Prof Sun Qiang, PhD, Andrew Siroka, PhD, Sedona Sweeney, MSc, Stéphane Verguet, PhD, Nimalan Arinaminpathy, DPhil, Andrew S Azman, PhD, Eran Bendavid, MD, Stewart T Chang, PhD, Prof Ted Cohen, DPH, Justin T Denholm, PhD, David W Dowdy, MD, Philip A Eckhoff, PhD, Jeremy D Goldhaber-Fiebert, PhD, Andreas Handel, PhD, Grace H Huynh, PhD, Marek Lalli, MSc, Hsien-Ho Lin, ScD, Sandip Mandal, PhD, Emma S McBryde, PhD, Surabhi Pandey, PhD, Prof Joshua A Salomon, PhD, Sze-chuan Suen, MS, Tom Sumner, PhD, James M Trauer, MBBS, Bradley G Wagner, PhD, Prof Christopher C Whalen, MD, Chieh-Yin Wu, MS, Delia Boccia, PhD, Vineet K Chadha, MD, Salome Charalambous, PhD, Daniel P Chin, MD, Prof Gavin Churchyard, PhD, Colleen Daniels, MA, Puneet Dewan, MD, Lucica Ditiu, MD, Jeffrey W Eaton, PhD, Prof Alison D Grant, PhD, Piotr Hippner, MSc, Mehran Hosseini, MD, David Mametja, MPH, Carel Pretorius, PhD, Yogan Pillay, PhD, Kiran Rade, MD, Suvanand Sahu, MD, Lixia Wang, MS, Rein M G J Houben, PhD, Michael E Kimerling, MD, Richard G White, PhD, Anna Vassall, PhD


The post-2015 End TB Strategy sets global targets of reducing tuberculosis incidence by 50% and mortality by 75% by 2025. We aimed to assess resource requirements and cost-effectiveness of strategies to achieve these targets in China, India, and South Africa.

We examined intervention scenarios developed in consultation with country stakeholders, which scaled up existing interventions to high but feasible coverage by 2025. Nine independent modelling groups collaborated to estimate policy outcomes, and we estimated the cost of each scenario by synthesising service use estimates, empirical cost data, and expert opinion on implementation strategies. We estimated health effects (ie, disability-adjusted life-years averted) and resource implications for 2016–35, including patient-incurred costs. To assess resource requirements and cost-effectiveness, we compared scenarios with a base case representing continued current practice.

Incremental tuberculosis service costs differed by scenario and country, and in some cases they more than doubled existing funding needs. In general, expansion of tuberculosis services substantially reduced patient-incurred costs and, in India and China, produced net cost savings for most interventions under a societal perspective. In all three countries, expansion of access to care produced substantial health gains. Compared with current practice and conventional cost-effectiveness thresholds, most intervention approaches seemed highly cost-effective.

Expansion of tuberculosis services seems cost-effective for high-burden countries and could generate substantial health and economic benefits for patients, although substantial new funding would be required. Further work to determine the optimal intervention mix for each country is necessary.

Figure 2 Incremental patient-incurred costs for 2016–35, for each intervention scenario, compared with the base case, by country and model.


Bill and Melinda Gates Foundation


Choosing a limited set of sensor locations to characterize or classify a high-dimensional system is an important challenge in engineering design. Traditionally, optimizing the sensor locations involves a brute-force, combinatorial search, which is NP-hard and is computationally intractable for even moderately large problems. Using recent advances in sparsity-promoting techniques, we present a novel algorithm to solve this sparse sensor placement optimization for classification (SSPOC) that exploits low-dimensional structure exhibited by many high-dimensional systems. Our approach is inspired by compressed sensing, a framework that reconstructs data from few measurements. If only classification is required, reconstruction can be circumvented and the measurements needed are orders-of-magnitude fewer still. Our algorithm solves an $\ell_1$ minimization to find the fewest nonzero entries of the full measurement vector that exactly reconstruct the discriminant vector in feature space; these entries represent sensor locations that best inform the decision task. We demonstrate the SSPOC algorithm on five classification tasks, using datasets from a diverse set of examples, including physical dynamical systems, image recognition, and microarray cancer identification. Once training identifies sensor locations, data taken at these locations forms a low-dimensional measurement space, and we perform computationally efficient classification with accuracy approaching that of classification using full-state data. The algorithm also works when trained on heavily subsampled data, eliminating the need for unrealistic full-state training data.

Dr Rein M G J Houben, PhD, Nicolas A Menzies, PhD, Tom Sumner, PhD, Grace H Huynh, PhD, Nimalan Arinaminpathy, PhD, Jeremy D Goldhaber-Fiebert, PhD, Hsien-Ho Lin, PhD, Chieh-Yin Wu, MS, Sandip Mandal, PhD, Surabhi Pandey, PhD, Sze-chuan Suen, MS, Eran Bendavid, MD, Andrew S Azman, PhD, David W Dowdy, PhD, Nicolas Bacaër, PhD, Allison S Rhines, PhD, Prof Marcus W Feldman, PhD, Andreas Handel, PhD, Prof Christopher C Whalen, MD, Stewart T Chang, PhD, Bradley G Wagner, PhD, Philip A Eckhoff, PhD, James M Trauer, PhD, Justin T Denholm, PhD, Prof Emma S McBryde, PhD, Ted Cohen, DPH, Prof Joshua A Salomon, PhD, Carel Pretorius, PhD, Marek Lalli, MSc, Jeffrey W Eaton, PhD, Delia Boccia, PhD, Mehran Hosseini, MD, Gabriela B Gomez, PhD, Suvanand Sahu, MD, Colleen Daniels, MA, Lucica Ditiu, MD, Daniel P Chin, MD, Lixia Wang, MS, Vineet K Chadha, MD, Kiran Rade, MPhil, Puneet Dewan, MD, Piotr Hippner, MSc, Salome Charalambous, PhD, Prof Alison D Grant, Prof Gavin Churchyard, PhD, Yogan Pillay, PhD, L David Mametja, MPH, Michael E Kimerling, MD, Anna Vassall, PhD, Richard G White, PhD


The post-2015 End TB Strategy proposes targets of 50% reduction in tuberculosis incidence and 75% reduction in mortality from tuberculosis by 2025. We aimed to assess whether these targets are feasible in three high-burden countries with contrasting epidemiology and previous programmatic achievements.

11 independently developed mathematical models of tuberculosis transmission projected the epidemiological impact of currently available tuberculosis interventions for prevention, diagnosis, and treatment in China, India, and South Africa. Models were calibrated with data on tuberculosis incidence and mortality in 2012. Representatives from national tuberculosis programmes and the advocacy community provided distinct country-specific intervention scenarios, which included screening for symptoms, active case finding, and preventive therapy.

Aggressive scale-up of any single intervention scenario could not achieve the post-2015 End TB Strategy targets in any country. However, the models projected that, in the South Africa national tuberculosis programme scenario, a combination of continuous isoniazid preventive therapy for individuals on antiretroviral therapy, expanded facility-based screening for symptoms of tuberculosis at health centres, and improved tuberculosis care could achieve a 55% reduction in incidence (range 31–62%) and a 72% reduction in mortality (range 64–82%) compared with 2015 levels. For India, and particularly for China, full scale-up of all interventions in tuberculosis-programme performance fell short of the 2025 targets, despite preventing a cumulative 3·4 million cases. The advocacy scenarios illustrated the high impact of detecting and treating latent tuberculosis.

Major reductions in tuberculosis burden seem possible with current interventions. However, additional interventions, adapted to country-specific tuberculosis epidemiology and health systems, are needed to reach the post-2015 End TB Strategy targets at country level.