Modeling the spread of the Zika virus using topological data analysis

Topological data analysis in biomedicine: A review

Significant technological advances made in recent years have shepherded a dramatic increase in utilization of digital technologies for biomedicine- everything from the widespread use of electronic health records to improved medical imaging capabilities and the rising ubiquity of genomic sequencing contribute to a "digitization" of biomedical research and clinical care. With this shift toward computerized tools comes a dramatic increase in the amount of available data, and current tools for data analysis capable of extracting meaningful knowledge from this wealth of information have yet to catch up. This article seeks to provide an overview of emerging mathematical methods with the potential to improve the abilities of clinicians and researchers to analyze biomedical data, but may be hindered from doing so by a lack of conceptual accessibility and awareness in the life sciences research community. In particular, we focus on topological data analysis (TDA), a set of methods grounded in the mathematical field of algebraic topology that seeks to describe and harness features related to the "shape" of data. We aim to make such techniques more approachable to non-mathematicians by providing a conceptual discussion of their theoretical foundations followed by a survey of their published applications to scientific research. Finally, we discuss the limitations of these methods and suggest potential avenues for future work integrating mathematical tools into clinical care and biomedical informatics.

Noise robustness of persistent homology on greyscale images, across filtrations and signatures

Topological data analysis is a recent and fast growing field that approaches the analysis of datasets using techniques from (algebraic) topology. Its main tool, persistent homology (PH), has seen a notable increase in applications in the last decade. Often cited as the most favourable property of PH and the main reason for practical success are the stability theorems that give theoretical results about noise robustness, since real data is typically contaminated with noise or measurement errors. However, little attention has been paid to what these stability theorems mean in practice. To gain some insight into this question, we evaluate the noise robustness of PH on the MNIST dataset of greyscale images. More precisely, we investigate to what extent PH changes under typical forms of image noise, and quantify the loss of performance in classifying the MNIST handwritten digits when noise is added to the data. The results show that the sensitivity to noise of PH is influenced by the choice of filtrations and persistence signatures (respectively the input and output of PH), and in particular, that PH features are often not robust to noise in a classification task.

Topological data analysis model for the spread of the coronavirus

We apply topological data analysis, specifically the Mapper algorithm, to the U.S. COVID-19 data. The resulting Mapper graphs provide visualizations of the pandemic that are more complete than those supplied by other, more standard methods. They allow for easy comparisons of the features of the pandemic across time and space and encode a variety of geometric features of the data cloud created from geographic information, time progression, and the number of COVID-19 cases. The Mapper graphs reflect the development of the pandemic across all of the U.S. and capture the growth rates as well as the regional prominence of hot-spots.

Arbovirus vectors of epidemiological concern in the Americas: A scoping review of entomological studies on Zika, dengue and chikungunya virus vectors

Background

Three arthropod-borne viruses (arboviruses) causing human disease have been the focus of a large number of studies in the Americas since 2013 due to their global spread and epidemiological impacts: Zika, dengue, and chikungunya viruses. A large proportion of infections by these viruses are asymptomatic. However, all three viruses are associated with moderate to severe health consequences in a small proportion of cases. Two mosquito species, Aedes aegypti and Aedes albopictus, are among the world’s most prominent arboviral vectors, and are known vectors for all three viruses in the Americas.

Objectives

This review summarizes the state of the entomological literature surrounding the mosquito vectors of Zika, dengue and chikungunya viruses and factors affecting virus transmission. The rationale of the review was to identify and characterize entomological studies that have been conducted in the Americas since the introduction of chikungunya virus in 2013, encompassing a period of arbovirus co-circulation, and guide future research based on identified knowledge gaps.

Methods

The preliminary search for this review was conducted on PubMed (National Library of Health, Bethesda, MD, United States). The search included the terms ‘zika’ OR ‘dengue’ OR ‘chikungunya’ AND ‘vector’ OR ‘Aedes aegypti’ OR ‘Aedes albopictus’. The search was conducted on March 1^st of 2018, and included all studies since January 1^st of 2013.

Results

A total of 96 studies were included in the scoping review after initial screening and subsequent exclusion of out-of-scope studies, secondary data publications, and studies unavailable in English language.

Key findings

We observed a steady increase in number of publications, from 2013 to 2018, with half of all studies published from January 2017 to March 2018. Interestingly, information on Zika virus vector species composition was abundant, but sparse on Zika virus transmission dynamics. Few studies examined natural infection rates of Zika virus, vertical transmission, or co-infection with other viruses. This is in contrast to the wealth of research available on natural infection and co-infection for dengue and chikungunya viruses, although vertical transmission research was sparse for all three viruses.

Vector distribution and transmission risk of the Zika virus in South and Central America

Background

Zika is of great medical relevance due to its rapid geographical spread in 2015 and 2016 in South America and its serious implications, for example, certain birth defects. Recent epidemics urgently require a better understanding of geographic patterns of the Zika virus transmission risk. This study aims to map the Zika virus transmission risk in South and Central America. We applied the maximum entropy approach, which is common for species distribution modelling, but is now also widely in use for estimating the geographical distribution of infectious diseases.

Methods

As predictor variables we used a set of variables considered to be potential drivers of both direct and indirect effects on the emergence of Zika. Specifically, we considered (a) the modelled habitat suitability for the two main vector species Aedes aegypti and Ae. albopictus as a proxy of vector species distributions; (b) temperature, as it has a great influence on virus transmission; (c) commonly called evidence consensus maps (ECM) of human Zika virus infections on a regional scale as a proxy for virus distribution; (d) ECM of human dengue virus infections and, (e) as possibly relevant socio-economic factors, population density and the gross domestic product.

Results

The highest values for the Zika transmission risk were modelled for the eastern coast of Brazil as well as in Central America, moderate values for the Amazon basin and low values for southern parts of South America. The following countries were modelled to be particularly affected: Brazil, Colombia, Cuba, Dominican Republic, El Salvador, Guatemala, Haiti, Honduras, Jamaica, Mexico, Puerto Rico and Venezuela. While modelled vector habitat suitability as predictor variable showed the highest contribution to the transmission risk model, temperature of the warmest quarter contributed only comparatively little. Areas with optimal temperature conditions for virus transmission overlapped only little with areas of suitable habitat conditions for the two main vector species. Instead, areas with the highest transmission risk were characterised as areas with temperatures below the optimum of the virus, but high habitat suitability modelled for the two main vector species.

Conclusion

Modelling approaches can help estimating the spatial and temporal dynamics of a disease. We focused on the key drivers relevant in the Zika transmission cycle (vector, pathogen, and hosts) and integrated each single component into the model. Despite the uncertainties generally associated with modelling, the approach applied in this study can be used as a tool and assist decision making and managing the spread of Zika.

A roadmap for the computation of persistent homology

Persistent homology (PH) is a method used in topological data analysis (TDA) to study qualitative features of data that persist across multiple scales. It is robust to perturbations of input data, independent of dimensions and coordinates, and provides a compact representation of the qualitative features of the input. The computation of PH is an open area with numerous important and fascinating challenges. The field of PH computation is evolving rapidly, and new algorithms and software implementations are being updated and released at a rapid pace. The purposes of our article are to (1) introduce theory and computational methods for PH to a broad range of computational scientists and (2) provide benchmarks of state-of-the-art implementations for the computation of PH. We give a friendly introduction to PH, navigate the pipeline for the computation of PH with an eye towards applications, and use a range of synthetic and real-world data sets to evaluate currently available open-source implementations for the computation of PH. Based on our benchmarking, we indicate which algorithms and implementations are best suited to different types of data sets. In an accompanying tutorial, we provide guidelines for the computation of PH. We make publicly available all scripts that we wrote for the tutorial, and we make available the processed version of the data sets used in the benchmarking.

ELECTRONIC SUPPLEMENTARY MATERIAL

The online version of this article (doi:10.1140/epjds/s13688-017-0109-5) contains supplementary material.