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EXPLORE IDM’S CURRENT RESEARCH PUBLICATIONS

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EPJ

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

SCIENCE TRANSLATIONAL MEDICINE

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 LANCET

Background
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.

Methods
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.

Findings
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.

Interpretation
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.

Funding

Bill and Melinda Gates Foundation


SIAM JOURNAL OF APPLIED MATHEMATICS

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 LANCET

Background
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.

Methods
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.

Findings
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.

Interpretation
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.

Kevin A. McCarthy, Guillaume Chabot-Couture, and Faisal Shuaib

A SPATIAL MODEL OF WILD POLIOVIRUS TYPE 1 IN KANO STATE, NIGERIA

Background
Since the launch of the Global Polio Eradication Initiative, all but three countries (Nigeria, Pakistan, and Afghanistan) have apparently interrupted all wild poliovirus (WPV) transmission, and only one of three wild serotypes has been reported globally since 2012. Countrywide supplemental immunization campaigns in Nigeria produced dramatic reduction in WPV Type 1 paralysis cases since 2010 compared to the 2000’s, and WPV1 has not been observed in Nigeria since July 24, 2014. This article presents the development and calibration of a spatial metapopulation model of wild poliovirus Type 1 transmission in Kano State, Nigeria, which was the location of the most recent WPV1 case and 5 out of 6 of the reported WPV1 paralytic cases in Nigeria in 2014.

Methods
The model is calibrated to data on the case counts and age at onset of paralysis from 2003–2009. The features of the data drive model development from a simple susceptible-exposed-infective-recovered (SEIR) model to a spatial metapopulation model featuring seasonal forcing and age-dependent transmission. The calibrated parameter space is then resampled, projected forward, and compared to more recent case counts to estimate the probability that Type 1 poliovirus has been eliminated in Kano state.

Results
The model indicates a 91 % probability that Type 1 poliovirus has been eliminated from Kano state as of October 2015. This probability rises to >99 % if no WPV1 paralysis cases are detected for another year. The other states in Nigeria have experienced even longer case-free periods (the only other state with a WPV1 case was Yobe, on April 19, 2014), and Nigeria is the last remaining country in Africa to experience endemic WPV1 transmission, so these results can be interpreted as an upper bound on the probability that WPV1 transmission is currently interrupted continent-wide.

Conclusions
While the results indicate optimism that WPV1 transmission has been interrupted in Kano state, the model also assumes that frequent SIAs with high coverage continue to take place in Kano state through the end of the certification period. We conclude that though WPV1 appears to be on the brink of continent-wide elimination (WHO officially removed Nigeria from the list of polio-endemic countries on September 25, 2015), it is important for the polio program to maintain vigilance in surveillance and vaccination activities to prevent WPV1 resurgence through the WHO’s 3-year eradication certification period.

MALARIA JOURNAL

Background
The burden of falciparum malaria remains unacceptably high in much of sub-Saharan Africa and massive efforts are underway to eliminate the parasite. While symptoms of malaria are caused by asexual reproduction of the parasite, transmission to new human hosts relies entirely on male and female sexual-stage parasites, known as gametocytes. Successful transmission can be observed at very low gametocyte densities, which raises the question of whether transmission-enhancing mechanisms exist in the human host, the mosquito, or both.

Methods
A new computational model was developed to investigate the probability of fertilization over a range of overdispersion parameters and male gamete exploration rates. Simulations were used to fit a likelihood surface for data on rates of mosquito infection across a wide range of host gametocyte densities.

Results
The best fit simultaneously requires very strong overdispersion and faster gamete exploration than is possible with random swimming in order to explain typical prevalence levels in mosquitoes. Gametocyte overdispersion or clustering in the human host and faster gamete exploration of the mosquito blood meal are highly probably given these results

Conclusions
Density-dependent gametocyte clustering in the human host, and non-random searching (e.g., chemotaxis) in the mosquito are probable. Future work should aim to discover these mechanisms, as disrupting parasite development in the mosquito will play a critical role in eliminating malaria.

PHYSICAL REVIEW E

In recent years, many variants of percolation have been used to study network structure and the behavior of processes spreading on networks. These include bond percolation, site percolation, k-core percolation, bootstrap percolation, the generalized epidemic process, and the Watts threshold model (WTM). We show that—except for bond percolation—each of these processes arises as a special case of the WTM, and bond percolation arises from a small modification. In fact “heterogeneous k-core percolation,” a corresponding “heterogeneous bootstrap percolation” model, and the generalized epidemic process are completely equivalent to one another and the WTM. We further show that a natural generalization of the WTM in which individuals “transmit” or “send a message” to their neighbors with some probability less than 1 can be reformulated in terms of the WTM, and so this apparent generalization is in fact not more general. Finally, we show that in bond percolation, finding the set of nodes in the component containing a given node is equivalent to finding the set of nodes activated if that node is initially activated and the node thresholds are chosen from the appropriate distribution. A consequence of these results is that mathematical techniques developed for the WTM apply to these other models as well, and techniques that were developed for some particular case may in fact apply much more generally.

ARXIV

We consider the application of Koopman theory to nonlinear partial differential equations. We demonstrate that the observables chosen for constructing the Koopman operator are critical for enabling an accurate approximation to the nonlinear dynamics. If such observables can be found, then the dynamic mode decomposition algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues and Koopman modes. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on two canonical, nonlinear PDEs: Burgers’ equation and the nonlinear Schr¨odinger equation. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.

AMERICAN CONTROL CONFERENCE (ACC)

Given a network, we would like to determine which subset of nodes should be measured by limited sensing facilities to maximize information about the entire network. The optimal choice corresponds to the configuration that returns the highest value of a measure of observability of the system. Here, the determinant of the inverse of the observability Gramian is used to evaluate the degree of observability. Additionally, the effects of changes in the topology of the corresponding graph of a network on the observability of the network are investigated. The theory is illustrated on the problem of detection of an epidemic disease in a community. The purpose here is to find the smallest number of people who must be examined to predict the number of infected people in an arbitrary community. Results are demonstrated in simulation.