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Getz, Wayne M.; Salter, Richard; Vissat, Ludovica Luisa(
, BMC Medical Education)
AbstractBackground
An understanding of epidemiological dynamics, once confined to mathematical epidemiologists and applied mathematicians, can be disseminated to a non-mathematical community of health care professionals and applied biologists through simple-to-use simulation applications. We used Numerus Model Builder RAMPⓇ(Runtime Alterable Model Platform) technology, to construct deterministic and stochastic versions of compartmental SIR (Susceptible, Infectious, Recovered with immunity) models as simple-to-use, freely available, epidemic simulation application programs.
Results
We take the reader through simulations used to demonstrate the following concepts: 1) disease prevalence curves of unmitigated outbreaks have a single peak and result in epidemics that ‘burn’ through the population to become extinguished when the proportion of the susceptible population drops below a critical level; 2) if immunity in recovered individuals wanes sufficiently fast then the disease persists indefinitely as an endemic state, with possible dampening oscillations following the initial outbreak phase; 3) the steepness and initial peak of the prevalence curve are influenced by the basic reproductive valueR0, which must exceed 1 for an epidemic to occur; 4) the probability that a single infectious individual in a closed population (i.e. no migration) gives rise to an epidemic increases with the value ofR0>1; 5) behavior that adaptively decreases the contact rate among individuals with increasing prevalence has major effects on the prevalence curve including dramatic flattening of the prevalence curve along with the generation of multiple prevalence peaks; 6) the impacts of treatment are complicated to model because they effect multiple processes including transmission, recovery and mortality; 7) the impacts of vaccination policies, constrained by a fixed number of vaccination regimens and by the rate and timing of delivery, are crucially important to maximizing the ability of vaccination programs to reduce mortality.
Conclusion
Our presentation makes transparent the key assumptions underlying SIR epidemic models. Our RAMP simulators are meant to augment rather than replace classroom material when teaching epidemiological dynamics. They are sufficiently versatile to be used by students to address a range of research questions for term papers and even dissertations.
Dougherty, Eric R.; Seidel, Dana P.; Blackburn, Jason K.; Turner, Wendy C.; Getz, Wayne M.(
, Movement Ecology)
Abstract
Movement behavior is an important contributor to habitat selection and its incorporation in disease risk models has been somewhat neglected. The habitat preferences of host individuals affect their probability of exposure to pathogens. If preference behavior can be incorporated in ecological niche models (ENMs) when data on pathogen distributions are available, then variation in such behavior may dramatically impact exposure risk. Here we use data from the anthrax endemic system of Etosha National Park, Namibia, to demonstrate how integrating inferred movement behavior alters the construction of disease risk maps. We used a Maximum Entropy (MaxEnt) model that associated soil, bioclimatic, and vegetation variables with the best available pathogen presence data collected at anthrax carcass sites to map areas of most likelyBacillus anthracis(the causative bacterium of anthrax) persistence. We then used a hidden Markov model (HMM) to distinguish foraging and non-foraging behavioral states along the movement tracks of nine zebra (Equus quagga) during the 2009 and 2010 anthrax seasons. The resulting tracks, decomposed on the basis of the inferred behavioral state, formed the basis of step-selection functions (SSFs) that used the MaxEnt output as a potential predictor variable. Our analyses revealed different risks of exposure during different zebra behavioral states, which were obscured when the full movement tracks were analyzed without consideration of the underlying behavioral states of individuals. Pathogen (or vector) distribution models may be misleading with regard to the actual risk faced by host animal populations when specific behavioral states are not explicitly accounted for in selection analyses. To more accurately evaluate exposure risk, especially in the case of environmentally transmitted pathogens, selection functions could be built for each identified behavioral state and then used to assess the comparative exposure risk across relevant states. The scale of data collection and analysis, however, introduces complexities and limitations for consideration when interpreting results.
McCoy, David; Mgbara, Whitney; Horvitz, Nir; Getz, Wayne M.; Hubbard, Alan(
, Scientific Reports)
Abstract Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) the causal agent for COVID-19, is a communicable disease spread through close contact. It is known to disproportionately impact certain communities due to both biological susceptibility and inequitable exposure. In this study, we investigate the most important health, social, and environmental factors impacting the early phases (before July, 2020) of per capita COVID-19 transmission and per capita all-cause mortality in US counties. We aggregate county-level physical and mental health, environmental pollution, access to health care, demographic characteristics, vulnerable population scores, and other epidemiological data to create a large feature set to analyze per capita COVID-19 outcomes. Because of the high-dimensionality, multicollinearity, and unknown interactions of the data, we use ensemble machine learning and marginal prediction methods to identify the most salient factors associated with several COVID-19 outbreak measure. Our variable importance results show that measures of ethnicity, public transportation and preventable diseases are the strongest predictors for both per capita COVID-19 incidence and mortality. Specifically, the CDC measures for minority populations, CDC measures for limited English, and proportion of Black- and/or African-American individuals in a county were the most important features for per capita COVID-19 cases within a month after the pandemic started in a county and also at the latest date examined. For per capita all-cause mortality at day 100 and total to date, we find that public transportation use and proportion of Black- and/or African-American individuals in a county are the strongest predictors. The methods predict that, keeping all other factors fixed, a 10% increase in public transportation use, all other factors remaining fixed at the observed values, is associated with increases mortality at day 100 of 2012 individuals (95% CI [1972, 2356]) and likewise a 10% increase in the proportion of Black- and/or African-American individuals in a county is associated with increases total deaths at end of study of 2067 (95% CI [1189, 2654]). Using data until the end of study, the same metric suggests ethnicity has double the association as the next most important factors, which are location, disease prevalence, and transit factors. Our findings shed light on societal patterns that have been reported and experienced in the U.S. by using robust methods to understand the features most responsible for transmission and sectors of society most vulnerable to infection and mortality. In particular, our results provide evidence of the disproportionate impact of the COVID-19 pandemic on minority populations. Our results suggest that mitigation measures, including how vaccines are distributed, could have the greatest impact if they are given with priority to the highest risk communities.
Getz, Wayne M.; Salter, Richard; Luisa Vissat, Ludovica; Koopman, James S.; Simon, Carl P.(
, Journal of The Royal Society Interface)
We present methods for building a Java Runtime-Alterable-Model Platform (RAMP) of complex dynamical systems. We illustrate our methods by building a multivariant SEIR (epidemic) RAMP. Underlying our RAMP is an individual-based model that includes adaptive contact rates, pathogen genetic drift, waning and cross-immunity. Besides allowing parameter values, process descriptions and scriptable runtime drivers to be easily modified during simulations, our RAMP can used within R-Studio and other computational platforms. Process descriptions that can be runtime altered within our SEIR RAMP include pathogen variant-dependent host shedding, environmental persistence, host transmission and within-host pathogen mutation and replication. They also include adaptive social distancing and adaptive application of vaccination rates and variant-valency of vaccines. We present simulation results using parameter values and process descriptions relevant to the current COVID-19 pandemic. Our results suggest that if waning immunity outpaces vaccination rates, then vaccination rollouts may fail to contain the most transmissible variants, particularly if vaccine valencies are not adapted to deal with escape mutations. Our SEIR RAMP is designed for easy use by others. More generally, our RAMP concept facilitates construction of highly flexible complex systems models of all types, which can then be easily shared as stand-alone application programs.
Getz, Wayne M.; Salter, Richard; Luisa Vissat, Ludovica; Horvitz, Nir(
, Journal of Translational Medicine)
AbstractBackground
No versatile web app exists that allows epidemiologists and managers around the world to comprehensively analyze the impacts of COVID-19 mitigation. Thehttp://covid-webapp.numerusinc.com/web app presented here fills this gap.
Methods
Our web app uses a model that explicitly identifies susceptible, contact, latent, asymptomatic, symptomatic and recovered classes of individuals, and a parallel set of response classes, subject to lower pathogen-contact rates. The user inputs a CSV file of incidence and, if of interest, mortality rate data. A default set of parameters is available that can be overwritten through input or online entry, and a user-selected subset of these can be fitted to the model using maximum-likelihood estimation (MLE). Model fitting and forecasting intervals are specifiable and changes to parameters allow counterfactual and forecasting scenarios. Confidence or credible intervals can be generated using stochastic simulations, based on MLE values, or on an inputted CSV file containing Markov chain Monte Carlo (MCMC) estimates of one or more parameters.
Results
We illustrate the use of our web app in extracting social distancing, social relaxation, surveillance or virulence switching functions (i.e., time varying drivers) from the incidence and mortality rates of COVID-19 epidemics in Israel, South Africa, and England. The Israeli outbreak exhibits four distinct phases: initial outbreak, social distancing, social relaxation, and a second wave mitigation phase. An MCMC projection of this latter phase suggests the Israeli epidemic will continue to produce into late November an average of around 1500 new case per day, unless the population practices social-relaxation measures at least 5-fold below the level in August, which itself is 4-fold below the level at the start of July. Our analysis of the relatively late South African outbreak that became the world’s fifth largest COVID-19 epidemic in July revealed that the decline through late July and early August was characterised by a social distancing driver operating at more than twice the per-capita applicable-disease-class (pc-adc) rate of the social relaxation driver. Our analysis of the relatively early English outbreak, identified a more than 2-fold improvement in surveillance over the course of the epidemic. It also identified a pc-adc social distancing rate in early August that, though nearly four times the pc-adc social relaxation rate, appeared to barely contain a second wave that would break out if social distancing was further relaxed.
Conclusion
Our web app provides policy makers and health officers who have no epidemiological modelling or computer coding expertise with an invaluable tool for assessing the impacts of different outbreak mitigation policies and measures. This includes an ability to generate an epidemic-suppression or curve-flattening index that measures the intensity with which behavioural responses suppress or flatten the epidemic curve in the region under consideration.
Huang, Yen-Hua; Joel, Hendrina; Küsters, Martina; Barandongo, Zoe R.; Cloete, Claudine C.; Hartmann, Axel; Kamath, Pauline L.; Kilian, J. Werner; Mfune, John K.; Shatumbu, Gabriel; et al(
, Proceedings of the Royal Society B: Biological Sciences)
null
(Ed.)
When a transmission hotspot for an environmentally persistent pathogen establishes in otherwise high-quality habitat, the disease may exert a strong impact on a host population. However, fluctuating environmental conditions lead to heterogeneity in habitat quality and animal habitat preference, which may interrupt the overlap between selected and risky habitats. We evaluated spatio-temporal patterns in anthrax mortalities in a plains zebra ( Equus quagga ) population in Etosha National Park, Namibia, incorporating remote-sensing and host telemetry data. A higher proportion of anthrax mortalities of herbivores was detected in open habitats than in other habitat types. Resource selection functions showed that the zebra population shifted habitat selection in response to changes in rainfall and vegetation productivity. Average to high rainfall years supported larger anthrax outbreaks, with animals congregating in preferred open habitats, while a severe drought forced animals into otherwise less preferred habitats, leading to few anthrax mortalities. Thus, the timing of anthrax outbreaks was congruent with preference for open plains habitats and a corresponding increase in pathogen exposure. Given shifts in habitat preference, the overlap in high-quality habitat and high-risk habitat is intermittent, reducing the adverse consequences for the population.
Greenbaum, Gili; Getz, Wayne M.; Rosenberg, Noah A.; Feldman, Marcus W.; Hovers, Erella; Kolodny, Oren(
, Nature Communications)
Abstract
Neanderthals and modern humans both occupied the Levant for tens of thousands of years prior to the spread of modern humans into the rest of Eurasia and their replacement of the Neanderthals. That the inter-species boundary remained geographically localized for so long is a puzzle, particularly in light of the rapidity of its subsequent movement. Here, we propose that infectious-disease dynamics can explain the localization and persistence of the inter-species boundary. We further propose, and support with dynamical-systems models, that introgression-based transmission of alleles related to the immune system would have gradually diminished this barrier to pervasive inter-species interaction, leading to the eventual release of the inter-species boundary from its geographic localization. Asymmetries between the species in the characteristics of their associated ‘pathogen packages’ could have generated feedback that allowed modern humans to overcome disease burden earlier than Neanderthals, giving them an advantage in their subsequent spread into Eurasia.
Miao, Zhongqi; Gaynor, Kaitlyn M.; Wang, Jiayun; Liu, Ziwei; Muellerklein, Oliver; Norouzzadeh, Mohammad Sadegh; McInturff, Alex; Bowie, Rauri C. K.; Nathan, Ran; Yu, Stella X.; et al(
, Scientific Reports)
Abstract
The implementation of intelligent software to identify and classify objects and individuals in visual fields is a technology of growing importance to operatives in many fields, including wildlife conservation and management. To non-experts, the methods can be abstruse and the results mystifying. Here, in the context of applying cutting edge methods to classify wildlife species from camera-trap data, we shed light on the methods themselves and types of features these methods extract to make efficient identifications and reliable classifications. The current state of the art is to employ convolutional neural networks (CNN) encoded within deep-learning algorithms. We outline these methods and present results obtained in training a CNN to classify 20 African wildlife species with an overall accuracy of 87.5% from a dataset containing 111,467 images. We demonstrate the application of a gradient-weighted class-activation-mapping (Grad-CAM) procedure to extract the most salient pixels in the final convolution layer. We show that these pixels highlight features in particular images that in some cases are similar to those used to train humans to identify these species. Further, we used mutual information methods to identify the neurons in the final convolution layer that consistently respond most strongly across a set of images of one particular species. We then interpret the features in the image where the strongest responses occur, and present dataset biases that were revealed by these extracted features. We also used hierarchical clustering of feature vectors (i.e., the state of the final fully-connected layer in the CNN) associated with each image to produce a visual similarity dendrogram of identified species. Finally, we evaluated the relative unfamiliarity of images that were not part of the training set when these images were one of the 20 species “known” to our CNN in contrast to images of the species that were “unknown” to our CNN.
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