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The biological and behavioral underpinnings of family planning (FP) unfold on an individual level, across a full reproductive life course, and within a complex system of social and structural constraints. Yet, much of the existing FP modeling landscape has focused solely on macro- or population-level dynamics of family planning. There is a need for an individual-based approach to provide a deeper understanding of how family planning is intertwined with individuals’ lives and health at the micro-level, which can contribute to more effective, person-centered design of both contraceptive technologies and programmatic interventions. This article introduces the Family Planning Simulator (FPsim), a data-driven, agent-based model of family planning, which explicitly models individual heterogeneity in biology and behavior over the life course. Agents in FPsim can experience a wide range of life-course events, such as increases in fecundability (and primary infertility), sexual debut, contraceptive choice, postpartum family planning, abortion, miscarriage, stillbirth, infant mortality, and maternal mortality. The core components of the model – fecundability and contraceptive choice, are represented individually and probabilistically, following age-specific patterns observed in demographic data and prospective cohort studies. Once calibrated to a setting leveraging multiple sources of data, FPsim can be used to build hypothetical scenarios and interrogate counterfactual research questions about the use, non-use, and/or efficacy of family planning programs and contraceptive methods. To our knowledge, FPsim is the first open-source, individual-level, woman-centered model of family planning.Author SummaryAlthough the causes and consequences of family planning unfold on an individual level, few models of family planning consider individual heterogeneity over the life course. To that end, we introduce the methodology, parameters, and use-case(s) of the family planning simulator (FPsim). FPsim is a data-driven agent-based model of family planning, which explicitly models individual heterogeneity in biology and behaviors over a woman’s full life course to better understand the micro-level dynamics leading to more or less successful family planning programs and policies. FPsim is a data-driven model that leverages multiple sources of data to simulate realistic populations in settings that reflect real-life contexts. It is designed to be flexible and user-friendly, allowing for custom calibrations and providing integrated functions for straightforward use. This manuscript describes the model design, including its parameters, potential data sources, and limitations. We illustrate the functionality of FPsim using hypothetical scenarios that improve upon existing injectable contraceptives and introduce new injectable contraceptives into a Senegal-like setting.

Understanding the complex interplay between human behavior, disease transmission and non-pharmaceutical interventions during the COVID-19 pandemic could provide valuable insights with which to focus future public health efforts. Cell phone mobility data offer a modern measurement instrument to investigate human mobility and behavior at an unprecedented scale. We investigate aggregated and anonymized mobility data, which measure how populations at the census-block-group geographic scale stayed at home in California, Georgia, Texas and Washington from the beginning of the pandemic. Using manifold learning techniques, we show that a low-dimensional embedding enables the identification of patterns of mobility behavior that align with stay-at-home orders, correlate with socioeconomic factors, cluster geographically, reveal subpopulations that probably migrated out of urban areas and, importantly, link to COVID-19 case counts. The analysis and approach provide local epidemiologists a framework for interpreting mobility data and behavior to inform policy makers’ decision-making aimed at curbing the spread of COVID-19. Combining human mobility data and nonlinear mathematical analysis techniques, this study offers insights into the interplay between human behavior, disease transmission and non-pharmaceutical interventions during the COVID-19 pandemic.

Background: The case count for coronavirus disease 2019 (COVID-19) is the predominant measure used to track epidemiological dynamics and inform policy decision-making. Case counts, however, are influenced by testing rates and strategies, which have varied over time and space. A method to interpret COVID-19 case counts consistently in the context of other surveillance data is needed, especially for data-limited settings in low- and middle-income countries (LMICs). Methods: Statistical analyses were used to detect changes in COVID-19 surveillance data. The pruned exact linear time change detection method was applied for COVID-19 case counts, number of tests, and test positivity rate over time. With this information, change points were categorized as likely driven by epidemiological dynamics or non-epidemiological influences, such as noise. Findings: Higher rates of epidemiological change detection are more associated with open testing policies than with higher testing rates. This study quantified alignment of non-pharmaceutical interventions with epidemiological changes. LMICs have the testing capacity to measure prevalence with precision if they use randomized testing. Rwanda stands out as a country with an efficient COVID-19 surveillance system. Subnational data reveal heterogeneity in epidemiological dynamics and surveillance. Interpretation: Relying solely on case counts to interpret pandemic dynamics has important limitations. Normalizing counts by testing rate mitigates some of these limitations, and an open testing policy is key to efficient surveillance. The study findings can be leveraged by public health officials to strengthen COVID-19 surveillance and support programmatic decision-making.

Genetic sequencing of malaria parasites has the potential to become an important tool in routine surveillance efforts for the control and eradication of malaria. For example, characterizing the epidemiological connectivity between different populations by assessing the genetic similarity of their parasites can offer insights for national malaria control programs and their strategic allocation of interventions. Despite the increase of whole-genome sequencing of malaria parasites, the development of a small set of single nucleotide polymorphisms (SNPs), often referred to as a barcode, or a panel of amplicons remains programmatically relevant for large-scale, local generation of genetic data. Here, we present an application of a machine-learning method to classify the geographic origin of a sampleandidentify a small set of region-specific SNPs. We demonstrate that this method can automatically identify sets of SNPs which complement the currently targeted loci from the malaria scientific community. More specifically, we find that many of these machine-learned SNPs are near known and well-studied loci such as regions and markers linked to drug resistance, while also identifying new areas of the genome where function is less characterized. The application of this technique can complement current approaches for selecting SNP locations and effectively scales with an increase in sample size.

Genomic data constitute a valuable adjunct to routine surveillance that can guide programmatic decisions to reduce the burden of infectious diseases. However, genomic capacities remain low in Africa. This study aims to operationalise a functional malaria molecular surveillance system in Mozambique for guiding malaria control and elimination.This prospective surveillance study seeks to generateThe protocol was reviewed and approved by the institutional (CISM) and national ethics committees of Mozambique (Comité Nacional de Bioética para Saúde) and Spain (Hospital Clinic of Barcelona). Project results will be presented to all stakeholders and published in open-access journals.NCT05306067.

Predicting ankle exoskeleton impacts on an individual’s walking function, stability, and efficiency remains challenging. Characterizing how the dynamics underlying center-of-mass (COM) mechanics and energetics change with exoskeletons may improve predictions of exoskeleton responses. We evaluated changes in individual-specific COM dynamics in unimpaired adults and one individual with post-stroke hemiparesis while walking in shoes-only and with passive ankle exoskeletons. We leveraged hybrid sparse identification of nonlinear dynamics (Hybrid-SINDy) – an equation-free data-driven method for inferring nonlinear hybrid dynamics using a large library of candidate functional forms – to identify functional forms that best modelled physical mechanisms describing leg-specific COM dynamics, termed template signatures. Across participants, Hybrid-SINDy identified template signatures comprised of leg stiffness and resting length, similar to common spring-loaded inverted pendulum models. Rotary stiffness mechanisms were identified in only 40-50% of participants. Unimpaired template signatures did not change with ankle exoskeletons (p > 0.13). Conversely, post-stroke paretic leg and rotary stiffness increased by 11% with zero- and high-stiffness exoskeleton, respectively, suggesting that COM dynamics may be more sensitive to exoskeletons following neurological injury. Agreement between our automatically-identified template signatures and those found from decades of biomechanics research supports Hybrid-SINDy’s potential to accelerate discovery of mechanisms underlying impaired locomotion and assistive device responses.

BackgroundDuring the first year of the COVID-19 pandemic, the most effective way to reduce transmission and to protect oneself was to reduce contact with others. However, it is unclear how behavior changed, despite numerous surveys about peoples’ attitudes and actions during the pandemic and public health efforts to influence behavior.MethodsWe used two sources of data to quantify changes in behavior at the county level during the first year of the pandemic in the United States: aggregated mobile device (smartphone) location data to approximate the fraction of people staying at home each day and digital invitation data to capture the number and size of social gatherings.ResultsBetween mid-March to early April 2020, the number of events fell and the fraction of devices staying at home peaked, independently of when states issued emergency orders or stay-at-home recommendations. Activity began to recover in May or June, with later rebounds in counties that suffered an early spring wave of reported COVID-19 cases. Counties with high incidence in the summer had more events, higher mobility, and less stringent state-level COVID-related restrictions the month before than counties with low incidence. Counties with high incidence in early fall stayed at home less and had less stringent state-level COVID-related restrictions in October, when cases began to rise in some parts of the US. During the early months of the pandemic, the number of events was inversely correlated with the fraction of devices staying at home, but after the fall of 2020 mobility appeared to stay constant as the number of events fell. Greater changes in behavior were observed in counties where a larger fraction voted for Biden in the 2020 US Presidential election. The number of people invited per event dropped gradually throughout the first year of the pandemic.ConclusionsThe mobility and events datasets uncovered different kinds of behavioral responses to the pandemic. Our results indicate that people did in fact change their behavior in ways that likely reduced COVID exposure and transmission, though the degree of change appeared to be affected by political views. Though the mobility data captured the initial massive behavior changes in the first months of the pandemic, the digital invitation data, presented here for the first time, continued to show large changes in behavior later in the first year of the pandemic.

Adolescent pregnancy is a known health risk to mother and child. Statements and reports of health outcomes typically group mothers under 20 years old together. Few studies examined this risk at a finer age resolution, none of them comprehensively, and with differing results.We analysed Demographic and Health Surveys data from 2004 to 2018 in sub-Saharan Africa (SSA) and South Asia, on firstborn children of mothers 25 years old or younger. We examined the association between maternal age and stillbirths, and neonatal mortality rate (NNMR), infant mortality rate (IMR) and under-5 mortality rate (U5MR), using mixed-effects logistic regression adjusting for major demographic variables and exploring the impact of maternal health-seeking.In both regions and across all endpoints, mortality rates of children born to mothers aged16 years, 16-17 years and 18-19 years at first birth were about 2-4 times, 1.5-2 times and 1.2-1.5 times higher, respectively, than among firstborn children of mothers aged 23-25. Absolute mortality rates declined over time, but the age gradient remained similar across time periods and regions. Adjusting for rural/urban residence and maternal education, in SSA in 2014-2018 having a16-year-old mother was associated with ORs of 3.71 (95% CI: 2.50 to 5.51) for stillbirth, 1.92 (1.60-2.30) for NNMR, 2.13 (1.85-2.46) for IMR and 2.39 (2.13-2.68) for U5MR, compared with having a mother aged 23-25. In South Asia, in 2014-2018 ORs were 5.12 (2.85-9.20) for stillbirth, 2.46 (2.03-2.97) for NNMR, 2.62 (2.22-3.08) for IMR and 2.59 (2.22-3.03) for U5MR. Part of the effect on NNMR and IMR may be mediated by a lower maternal health-seeking rate.Adolescent pregnancy is associated with dramatically worse child survival and mitigated by health-seeking behaviour, likely reflecting a combination of biological and social factors. Refining maternal age reporting will avoid masking the increased risk to children born to very young adolescent mothers. Collection of additional biological and social data may better reveal mediators of this relationship. Targeted intervention strategies to reduce unintended pregnancy at earlier ages may also improve child survival.

Molecular data and analysis outputs are being integrated into malaria surveillance efforts to provide valuable programmatic insights for national malaria control programs (NMCPs). A plethora of studies from diverse geographies have demonstrated that malaria parasite genetic data can be an important tool for drug resistance monitoring, species identification, outbreak analysis, and transmission characterization. Despite many successful research efforts, there are still important knowledge gaps hindering practical translation of each of these use cases for NMCPs. Here, we leverage epidemiological modeling and time-series data of 2035 genetic sequences collected in Thiès, Senegal from 2006-2018 to provide a quantitative and setting-specific assessment of the levels, trends, and connectivity of malaria transmission. We also identify the genetic features that are the most informative for inferring transmission in Thiès, such as the fraction of the population with multiple infections and the persistence of parasite lineages across multiple transmission seasons. The model fitting and uncertainty quantification framework also reveals a significant decrease in the level of malaria transmission around 2013. This difference coincides with a large-scale drought and bed net campaign by the NMCP and USAID and is independently corroborated by geo-spatial models of incidence in Thiès. We find that genetically identical samples are more likely to be geographically clustered even at the neighborhood scale; and moreover, these lineages propagate non-randomly around the city. Our approach and results provide quantitative guidance for the interpretation of malaria parasite genetic data from Thiès, Senegal and indicates the value of increased malaria genomic surveillance for NMCPs.

IntroductionAdolescent pregnancy is a known health risk to mother and child. Statements and reports of health outcomes typically group mothers under 20 years old together. Few studies examined this risk at a finer age resolution, none of them comprehensively, and with differing results.MethodsWe analyzed Demographic and Health Surveys (DHS) data from 2004-2018 in Sub-Saharan Africa (SSA) and South Asia, on firstborn children of mothers 25 years old or younger. We examined the association between maternal age and stillbirths, and rates of neonatal (NNMR), infant (IMR), and under-5 mortality (U5MR), using mixed-effects logistic regression adjusting for major demographic variables and exploring the impact of maternal health-seeking.ResultsIn both regions and across all endpoints, mortality rates of children born to mothers aged ConclusionsAdolescent pregnancy is associated with dramatically worse child survival and mitigated by health-seeking behavior, likely reflecting a combination of biological and social factors. Refining maternal age reporting will avoid masking the increased risk to children born to very young adolescent mothers. Collection of additional biological and social data may better reveal mediators of this relationship. Targeted intervention strategies to reduce unintended pregnancy at earlier ages may also improve child survival.What is already known?Most previous studies treat under-20 mothers as a single group when looking at risk of child health outcomes.Few studies have assessed the risk gradient versus age within this group, focusing only on neonatal and infant mortality rather than broader child survival outcomes.These studies found a higher risk of neonatal and infant mortality among younger adolescent mothers, even after adjusting for socio-economic, demographic and health service accessibility variables.The risk gradients for stillbirths and under-5 mortality outcomes of children born to adolescent mothers remain unexplored.What are the new findings?This is the most comprehensive, multi-regional study to-date that investigated the potential impacts of adolescent pregnancy, examining multiple child survival endpoints from stillbirths to under-5 mortality, and quantifying the risk gradient as a function of maternal age from adolescence through young adulthood.Children of mothers younger than 16 faced 2-4 times higher risk of death at all child mortality stages (stillbirths, neonatal, infant, and under-5) in both sub-Saharan Africa and South Asia regions.The association extends across socio-economic status (SES) groups in both urban and rural settings and stays consistent when controlling for maternal education and health seeking risk factors.What do the new findings imply?We recommend revision of maternal-age-group reporting conventions to make the increased child survival risk with adolescent pregnancy more visible.To improve child survival outcomes, improving health-seeking behavior and quality of maternal care, as well as targeted interventions to reduce unintended pregnancy among adolescents and mitigate its harmful consequences are needed.Collecting additional data on the social and biological aspects of adolescent pregnancy could help understand the impact size of these mediators on child health outcomes.

BackgroundScaling up access to safe, effective, and voluntary family planning (FP) services to achieve universal access for women and families will require increased commitment by countries and international organizations. On the way toward universal access, quantitative family planning goals have also been established by the United Nations through the sustainable development goals (SDGs). Here, we present a model-based framework that can help monitor progress toward these goals at the sub-national and demographic subgroup scale.MethodsWe utilize 90 demographic health surveys for 26 countries that contain associated geographic position system data. We extract survey cluster level data to fit multiple small area estimation models that estimate FP indicators by administrative unit one and two regions as well as different demographic subgroups.FindingsWe find significant variation of modern contraceptive prevalence rates (mCPR), unmet need, and demand satisfied by country, sub-national region, and demographic subgroup. Our model-based estimates show that on average for 436 administrative unit one regions, mCPR has increased at a rate of 0.75% per year and unmet need has decreased by 0.26% per year. There are also striking differences of FP indicators by demographic subgroup; for example, unmet need can be up to 40% different based on age and parity.InterpretationWe have developed a framework to help monitor progress, provide insights about the inequitable progress by region and demographic groups, and account for the sparsity of available data. These results and framework can help policy-makers better allocate and target interventions to help achieve family planning goals.FundingThis publication is based on models and data analysis performed by the Institute for Disease Modeling at the Bill & Melinda Gates Foundation.

0.1BackgroundCOVID-19 case counts are the predominant measure used to track epidemiological dynamics and inform policy decision-making. Case counts, however, are influenced by testing rates and strategies, which have varied over time and space. A method to consistently interpret COVID-19 case counts in the context of other surveillance data is needed, especially for data-limited settings in low- and middle-income countries (LMICs).0.2MethodsWe leverage statistical analyses to detect changes in COVID-19 surveillance data. We apply the pruned exact linear time change detection method for COVID-19 case counts, number of tests, and test positivity rate over time. With this information, we categorize change points as likely driven by epidemiological dynamics or non-epidemiological influences such as noise.0.3FindingsHigher rates of epidemiological change detection are more associated with open testing policies than with higher testing rates. We quantify alignment of non-pharmaceutical interventions with epidemiological changes. LMICs have the testing capacity to measure prevalence with precision if they use randomized testing. Rwanda stands out as a country with an efficient COVID-19 surveillance system. Sub-national data reveal heterogeneity in epidemiological dynamics and surveillance.0.4InterpretationRelying solely on case counts to interpret pandemic dynamics has important limitations. Normalizing counts by testing rate mitigates some of these limitations, and open testing policy is key to efficient surveillance. Our findings can be leveraged by public health officials to strengthen COVID-19 surveillance and support programmatic decision-making.0.5FundingThis publication is based on models and data analysis performed by the Institute for Disease Modeling at the Bill & Melinda Gates Foundation.Research in ContextEvidence before this studyWe searched for articles on the current practices, challenges, and proposals for COVID-19 surveillance in LMICs. We used Google Scholar with search terms including “COVID surveillance.” Existing studies were found to be qualitative, anecdotal, or highly location-specific.Added value of this studyWe developed a quantitative method that makes use of limited information available from LMICs. Our approach improves interpretation of epidemiological data and enables evaluation of COVID-19 surveillance dynamics across countries.Implications of all the available evidenceOur results demonstrate the importance of open testing for strong surveillance systems, bolstering existing anecdotal evidence. We show strong alignment across LMICs between non-pharmaceutical interventions and epidemiological changes. We demonstrate the importance of considering sub-national heterogeneity of epidemiological dynamics and surveillance.

Traditional clinical prediction models focus on parameters of the individual patient. For infectious diseases, sources external to the patient, including characteristics of prior patients and seasonal factors, may improve predictive performance. We describe the development of a predictive model that integrates multiple sources of data in a principled statistical framework using a post-test odds formulation. Our method enables electronic real-time updating and flexibility, such that components can be included or excluded according to data availability. We apply this method to the prediction of etiology of pediatric diarrhea, where “pre-test” epidemiologic data may be highly informative. Diarrhea has a high burden in low-resource settings, and antibiotics are often over-prescribed. We demonstrate that our integrative method outperforms traditional prediction in accurately identifying cases with a viral etiology, and show that its clinical application, especially when used with an additional diagnostic test, could result in a 61% reduction in inappropriately prescribed antibiotics.

As COVID-19 cases resurge in the United States, understanding the complex interplay between human behavior, disease transmission, and non-pharmaceutical interventions during the pandemic could provide valuable insights to focus future public health efforts. Cell-phone mobility data offers a modern measurement instrument to investigate human mobility and behavior at an unprecedented scale. We investigate mobility data collected, aggregated, and anonymized by SafeGraph Inc. which measures how populations at the census-block-group geographic scale stayed at home in California, Georgia, Texas, and Washington since the beginning of the pandemic. Using manifold learning techniques, we find patterns of mobility behavior that align with stay-at-home orders, correlate with socioeconomic factors, cluster geographically, and reveal sub-populations that likely migrated out of urban areas. The analysis and approach provides policy makers a framework for interpreting mobility data and behavior to inform actions aimed at curbing the spread of COVID-19.

In order to monitor progress towards malaria elimination, it is crucial to be able to measure changes in spatio-temporal transmission. However, common metrics of malaria transmission such as parasite prevalence are under powered in elimination contexts. China has achieved major reductions in malaria incidence and is on track to eliminate, having reporting zero locally-acquired malaria cases in 2017 and 2018. Understanding the spatio-temporal pattern underlying this decline, especially the relationship between locally-acquired and imported cases, can inform efforts to maintain elimination and prevent re-emergence. This is particularly pertinent in Yunnan province, where the potential for local transmission is highest. Using a geo-located individual-level dataset of cases recorded in Yunnan province between 2011 and 2016, we introduce a novel Bayesian framework to model a latent diffusion process and estimate the joint likelihood of transmission between cases and the number of cases with unobserved sources of infection. This is used to estimate the case reproduction number, Rc. We use these estimates within spatio-temporal geostatistical models to map how transmission varied over time and space, estimate the timeline to elimination and the risk of resurgence. We estimate the mean Rc between 2011 and 2016 to be 0.171 (95% CI = 0.165, 0.178) for P. vivax cases and 0.089 (95% CI = 0.076, 0.103) for P. falciparum cases. From 2014 onwards, no cases were estimated to have a Rc value above one. An unobserved source of infection was estimated to be moderately likely (p>0.5) for 19/ 611 cases and high (p>0.8) for 2 cases, suggesting very high levels of case ascertainment. Our estimates suggest that, maintaining current intervention efforts, Yunnan is unlikely to experience sustained local transmission up to 2020. However, even with a mean of 0.005 projected up to 2020, locally-acquired cases are possible due to high levels of importation., Author summary Although malaria is still responsible for a great deal of death and illness in many parts of the world, many national control programmes have made great strides in controlling malaria and now are in a position to aim for elimination. However, in order to monitor progress towards elimination and plan interventions, it is crucial to measure malaria transmission and how it varies over space and time. However, traditional metrics used to measure malaria transmission are not suitable in elimination settings. China is one example of a country approaching elimination, with aims to eliminate the disease by 2020. Using a detailed individual level dataset of the times and locations of people showing symptoms of malaria, we use approaches adapted from the study of how information spreads through social networks to estimate the likelihood of transmission occurring between cases. This information is used to estimate how many people we expect each case to go on to infect. In elimination settings, this number is an indication of how quickly elimination will be reached and how likely we are to see a resurgence in cases once elimination is achieved. Our results show a decline in this metric over time, as well as seasonal changes in transmission which are different to the patterns in when the most cases were observed.

Ambitious global goals have been established to provide universal access to affordable modern contraceptive methods. The UN's sustainable development goal 3.7.1 proposes satisfying the demand for family planning (FP) services by increasing the proportion of women of reproductive age using modern methods. To measure progress toward such goals in populous countries like Nigeria, it's essential to characterize the current levels and trends of FP indicators such as unmet need and modern contraceptive prevalence rates (mCPR). Moreover, the substantial heterogeneity across Nigeria and scale of programmatic implementation requires a sub-national resolution of these FP indicators. However, significant challenges face estimating FP indicators sub-nationally in Nigeria. In this article, we develop a robust, data-driven model to utilize all available surveys to estimate the levels and trends of FP indicators in Nigerian states for all women and by age-parity demographic subgroups. We estimate that overall rates and trends of mCPR and unmet need have remained low in Nigeria: the average annual rate of change for mCPR by state is 0.5% (0.4%,0.6%) from 2012-2017. Unmet need by age-parity demographic groups varied significantly across Nigeria; parous women express much higher rates of unmet need than nulliparous women. Our hierarchical Bayesian model incorporates data from a diverse set of survey instruments, accounts for survey uncertainty, leverages spatio-temporal smoothing, and produces probabilistic estimates with uncertainty intervals. Our flexible modeling framework directly informs programmatic decision-making by identifying age-parity-state subgroups with large rates of unmet need, highlights conflicting trends across survey instruments, and holistically interprets direct survey estimates., 27 pages, 16 figures

In previous work, we built a neuromechanical model for insect locomotion in the horizontal plane, containing a central pattern generator, motoneurons, muscles actuating jointed legs, and rudimentary proprioceptive feedback. This was subsequently simplified to a set of 24 phase oscillators describing motoneuronal activation of agonist-antagonist muscle pairs, which facilitates analyses and enables simulations over multi-dimensional parameter spaces. Here we use the phase-reduced model to study dynamics and stability over the typical speed range of the cockroach Blaberus discoidalis, the effects of feedback on response to perturbations, strategies for turning, and a trade-off between stability and maneuverability. We also compare model behavior with experiments on lateral perturbations, changes in body mass and moment of inertia, and climbing dynamics, and we present a simple control strategy for steering using exteroceptive feedback.

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately connected to Dynamic Mode Decomposition (DMD), a method that discovers spatial-temporal coherent modes from data, connects local-linear analysis to nonlinear operator theory, and importantly creates an equation-free architecture allowing investigation of complex systems. In actuated systems, standard Koopman analysis and DMD are incapable of producing input-output models; moreover, the dynamics and the modes will be corrupted by external forcing. Our new theoretical developments extend Koopman operator theory to allow for systems with nonlinear input-output characteristics. We show how this generalization is rigorously connected and generalizes a recent development called Dynamic Mode Decomposition with control (DMDc). We demonstrate this new theory on nonlinear dynamical systems, including a standard Susceptible-Infectious-Recovered model with relevance to the analysis of infectious disease data with mass vaccination (actuation)., 21 pages, 3 figures

China reported zero locally-acquired malaria cases in 2017 and 2018. Understanding the spatio-temporal pattern underlying this decline, especially the relationship between locally-acquired and imported cases, can inform efforts to maintain elimination and prevent re-emergence. This is particularly pertinent in Yunnan province, where the potential for local transmission is highest. Using a geo-located individual-level dataset of cases recorded in Yunnan province between 2011 and 2016, we jointly estimate the case reproduction number, Rc, and the number of unobserved sources of infection. We use these estimates within spatio-temporal geostatistical models to map how transmission varied over time and space, estimate the timeline to elimination and the risk of resurgence. Our estimates suggest that, maintaining current intervention efforts, Yunnan is unlikely to experience sustained local transmission up to 2020. However, even with a mean Rc of 0.005 projected for the year 2019, locally-acquired cases are possible due to high levels of importation.

The compartmental modeling software (CMS) is an open source computational framework that can simulate discrete, stochastic reaction models which are often utilized to describe complex systems from epidemiology and systems biology. In this article, we report the computational requirements, the novel input model language, the available numerical solvers, and the output file format for CMS. In addition, the CMS code repository also includes a library of example model files, unit and regression tests, and documentation. Two examples, one from systems biology and the other from computational epidemiology, are included that highlight the functionality of CMS. We believe the creation of computational frameworks such as CMS will advance our scientific understanding of complex systems as well as encourage collaborative efforts for code development and knowledge sharing.

The compartmental modeling software (CMS) is an open source computational framework that can simulate discrete, stochastic reaction models which are often utilized to describe complex systems from epidemiology and systems biology. In this article, we report the computational requirements, the novel input model language, the available numerical solvers, and the output file format for CMS. In addition, the CMS code repository also includes a library of example model files, unit and regression tests, and documentation. Two examples, one from systems biology and the other from computational epidemiology, are included that highlight the functionality of CMS. We believe the creation of computational frameworks such as CMS will advance our scientific understanding of complex systems as well as encourage collaborative efforts for code development and knowledge sharing.

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.

Inferring the structure and dynamics of network models is critical to understanding the functionality and control of complex systems, such as metabolic and regulatory biological networks. The increasing quality and quantity of experimental data enable statistical approaches based on information theory for model selection and goodness-of-fit metrics. We propose an alternative method to infer networked nonlinear dynamical systems by using sparsity-promoting $\ell_1$ optimization to select a subset of nonlinear interactions representing dynamics on a fully connected network. Our method generalizes the sparse identification of nonlinear dynamics (SINDy) algorithm to dynamical systems with rational function nonlinearities, such as biological networks. We show that dynamical systems with rational nonlinearities may be cast in an implicit form, where the equations may be identified in the null-space of a library of mixed nonlinearities including the state and derivative terms; this approach applies more generally to implicit dynamical systems beyond those containing rational nonlinearities. This method, implicit-SINDy, succeeds in inferring three canonical biological models: Michaelis-Menten enzyme kinetics, the regulatory network for competence in bacteria, and the metabolic network for yeast glycolysis., 11 pages, 6 figures

We develop a new method which extends Dynamic Mode Decomposition (DMD) to incorporate the effect of control to extract low-order models from high-dimensional, complex systems. DMD finds spatial-temporal coherent modes, connects local-linear analysis to nonlinear operator theory, and provides an equation-free architecture which is compatible with compressive sensing. In actuated systems, DMD is incapable of producing an input-output model; moreover, the dynamics and the modes will be corrupted by external forcing. Our new method, Dynamic Mode Decomposition with control (DMDc), capitalizes on all of the advantages of DMD and provides the additional innovation of being able to disambiguate between the underlying dynamics and the effects of actuation, resulting in accurate input-output models. The method is data-driven in that it does not require knowledge of the underlying governing equations, only snapshots of state and actuation data from historical, experimental, or black-box simulations. We demonstrate the method on high-dimensional dynamical systems, including a model with relevance to the analysis of infectious disease data with mass vaccination (actuation)., Comment: 10 pages, 4 figures

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.

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.

Hybrid systems are traditionally difficult to identify and analyze using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics (Hybrid-SINDy), which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty, and characterizes switching behavior. Specifically, we utilize the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass-spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviors is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots, and the protection of cyber infrastructures., 22 pages, 5 figures, 1 table. Code repository: https://github.com/niallmm/Hybrid-SINDy

We consider the application of Koopman theory to nonlinear partial differential equations and data-driven spatio-temporal systems. 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 (DMD) algorithm can be enacted to compute a finite-dimensional approximation of the Koopman operator, including its eigenfunctions, eigenvalues, and Koopman modes. We demonstrate simple rules of thumb for selecting a parsimonious set of observables that can greatly improve the approximation of the Koopman operator. Further, we show that the clear goal in selecting observables is to place the DMD eigenvalues on the imaginary axis, thus giving an objective function for observable selection. Judiciously chosen observables lead to physically interpretable spatio-temporal features of the complex system under consideration and provide a connection to manifold learning methods. Our method provides a valuable intermediate, yet interpretable, approximation to the Koopman operator that lies between the DMD method and the computationally intensive extended DMD (EDMD). We demonstrate the impact of observable selection, including kernel methods, and construction of the Koopman operator on several canonical nonlinear PDEs: Burgers’ equation, the nonlinear Schrödinger equation, the cubic-quintic Ginzburg-Landau equation, and a reaction-diffusion system. These examples serve to highlight the most pressing and critical challenge of Koopman theory: a principled way to select appropriate observables.

To study the effects of malaria-control interventions on parasite population genomics, we examined a set of 1,007 samples of the malaria parasite Plasmodium falciparum collected in Thies, Senegal between 2006 and 2013. The parasite samples were genotyped using a molecular barcode of 24 SNPs. About 35% of the samples grouped into subsets with identical barcodes, varying in size by year and sometimes persisting across years. The barcodes also formed networks of related groups. Analysis of 164 completely sequenced parasites revealed extensive sharing of genomic regions. In at least two cases we found first-generation recombinant offspring of parents whose genomes are similar or identical to genomes also present in the sample. An epidemiological model that tracks parasite genotypes can reproduce the observed pattern of barcode subsets. Quantification of likelihoods in the model strongly suggests a reduction of transmission from 2006–2010 with a significant rebound in 2012–2013. The reduced transmission and rebound were confirmed directly by incidence data from Thies. These findings imply that intensive intervention to control malaria results in rapid and dramatic changes in parasite population genomics. The results also suggest that genomics combined with epidemiological modeling may afford prompt, continuous, and cost-effective tracking of progress toward malaria elimination.

Background The development and application of quantitative methods to understand disease dynamics and plan interventions is becoming increasingly important in the push toward eradication of human infectious diseases, exemplified by the ongoing effort to stop the spread of poliomyelitis. Methods Dynamic mode decomposition (DMD) is a recently developed method focused on discovering coherent spatial-temporal modes in high-dimensional data collected from complex systems with time dynamics. The algorithm has a number of advantages including a rigorous connection to the analysis of nonlinear systems, an equation-free architecture, and the ability to efficiently handle high-dimensional data. Results We demonstrate the method on three different infectious disease sets including Google Flu Trends data, pre-vaccination measles in the UK, and paralytic poliomyelitis wild type-1 cases in Nigeria. For each case, we describe the utility of the method for surveillance and resource allocation. Conclusions We demonstrate how DMD can aid in the analysis of spatial-temporal disease data. DMD is poised to be an effective and efficient computational analysis tool for the study of infectious disease.

Although disease transmission in the near eradication regime is inherently stochastic, deterministic quantities such as the probability of eradication are of interest to policy makers and researchers. Rather than running large ensembles of discrete stochastic simulations over long intervals in time to compute these deterministic quantities, we create a data-driven and deterministic “coarse” model for them using the Equation Free (EF) framework. In lieu of deriving an explicit coarse model, the EF framework approximates any needed information, such as coarse time derivatives, by running short computational experiments. However, the choice of the coarse variables (i.e., the state of the coarse system) is critical if the resulting model is to be accurate. In this manuscript, we propose a set of coarse variables that result in an accurate model in the endemic and near eradication regimes, and demonstrate this on a compartmental model representing the spread of Poliomyelitis. When combined with adaptive time-stepping coarse projective integrators, this approach can yield over a factor of two speedup compared to direct simulation, and due to its lower dimensionality, could be beneficial when conducting systems level tasks such as designing eradication or monitoring campaigns.

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 $\ell_1$-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. A video abstract of this work may be found at: http://youtu.be/4tLSq_PEFms .

Complex systems exhibit dynamics that typically evolve on low-dimensional attractors and may have sparse representation in some optimal basis. Recently developed compressive sensing techniques exploit this sparsity for state reconstruction and/or categorical identification from limited measurements. We argue that data-driven dimensionality reduction methods integrate naturally with sparse sensing in the context of complex systems. This framework works equally well with a physical model or in an equation-free context, where data is available but the governing equations may be unknown. We demonstrate the advantages of combining these methods on three prototypical examples: classification of dynamical regimes, optimal sensor placement, and equation-free dynamic model reduction. These examples motivate the potentially transformative role that state-of-the-art data methods and machine learning can play in the analysis of complex systems.

Containing the recent West African outbreak of Ebola virus (EBOV) required the deployment of substantial global resources. Operationally, health workers and surveillance teams treated cases, collected genetic samples, and tracked case contacts. Despite the substantial progress in analyzing and modeling EBOV epidemiological data, a complete characterization of the spatiotemporal spread of Ebola cases remains a challenge. In this work, we offer a novel perspective on the EBOV epidemic that utilizes virus genome sequences to inform population-level, spatial models. Calibrated to phylogenetic linkages, these dynamic spatial models provide unique insight into the disease mobility of EBOV in Sierra Leone. Further, we developed a model selection framework that identifies important epidemiological variables influencing the spatiotemporal propagation of EBOV. Consistent with other investigations, our results show that the spread of EBOV during the beginning and middle portions of the epidemic strongly depended on the size of and distance between populations. Our analysis also revealed a substantial decline in the dependence on population size at the end of the epidemic, coinciding with the large-scale intervention campaign: Operation Western Area Surge. More generally, we believe this framework, pairing molecular diagnostics with dynamic models, has the potential to be a powerful forecasting tool along with offering operationally-relevant guidance for surveillance and sampling strategies during an epidemic., Comment: 15 pages, 12 figures

We develop an algorithm for model selection which allows for the consideration of a combinatorially large number of candidate models governing a dynamical system. The innovation circumvents a disadvantage of standard model selection which typically limits the number candidate models considered due to the intractability of computing information criteria. Using a recently developed sparse identification of nonlinear dynamics algorithm, the sub-selection of candidate models near the Pareto frontier allows for a tractable computation of AIC (Akaike information criteria) or BIC (Bayes information criteria) scores for the remaining candidate models. The information criteria hierarchically ranks the most informative models, enabling the automatic and principled selection of the model with the strongest support in relation to the time series data. Specifically, we show that AIC scores place each candidate model in the {\em strong support}, {\em weak support} or {\em no support} category. The method correctly identifies several canonical dynamical systems, including an SEIR (susceptible-exposed-infectious-recovered) disease model and the Lorenz equations, giving the correct dynamical system as the only candidate model with strong support., 14 pages, 6 figures, 1 algorithm

Despite the ever-increasing affordability and availability of high performance computing platforms, computational analysis of stochastic biochemical systems remains an open problem. A recently developed event-based parameter estimation method, the stochastic parameter search for events (SParSE), is able to efficiently sample reaction rate parameter values that confer a user-specified target event with a given probability and error tolerance. Despite the substantial computational savings, the efficiency of SParSE can be further improved by intelligently generating new initial parameter sets based on previously computed trajectories. In this article, we propose a principled method which combines the efficiencies of SParSE with these geometric machine-learning methods to generate new initial parameters based on the previously collected data.

Using a computational model of the Caenorhabditis elegans connectome dynamics, we show that proprioceptive feedback is necessary for sustained dynamic responses to external input. This is consistent with the lack of biophysical evidence for a central pattern generator, and recent experimental evidence that proprioception drives locomotion. The low-dimensional functional response of the Caenorhabditis elegans network of neurons to proprioception-like feedback is optimized by input of specific spatial wavelengths which correspond to the spatial scale of real body shape dynamics. Furthermore, we find that the motor subcircuit of the network is responsible for regulating this response, in agreement with experimental expectations. To explore how the connectomic dynamics produces the observed two-mode, oscillatory limit cycle behavior from a static fixed point, we probe the fixed point’s low-dimensional structure using Dynamic Mode Decomposition. This reveals that the nonlinear network dynamics encode six clusters of dynamic modes, with timescales spanning three orders of magnitude. Two of these six dynamic mode clusters correspond to previously-discovered behavioral modes related to locomotion. These dynamic modes and their timescales are encoded by the network’s degree distribution and specific connectivity. This suggests that behavioral dynamics are partially encoded within the connectome itself, the connectivity of which facilitates proprioceptive control., Author Summary The nematode C. elegans lives a complex and rich life despite having only 302 neurons. The full connectivity between these neurons (its “connectome”) has been measured, making it an ideal model system for understanding how neural processing generates behavior. However, unlike most animals, it doesn’t appear to have neural circuits dedicated to generating rhythmic motion. Even the simple rhythmic behavior of forward locomotion is believed to be ultimately driven by stretch-receptive proprioception as the worm changes body shape. Computational models of connectome dynamics can capture behavioral responses, making them valuable for studying neural dynamics. We consider a model of the full-connectome dynamics which, without external input, is in a static neural state. We show that proprioception-like input can bring the system into a rhythmic state similar to locomotion. We then show that arbitrary external inputs across all neurons can only excite some combination of six neural patterns, and that the shape and dynamics of these patterns are determined by the connectome. Furthermore, two of these patterns correspond to forward locomotion, such that the connectome facilitates locomotion-like responses. We thus find that the connectome itself is not random, but is ideally tuned for generating behavior.