Andres J. Garcia

A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of the world. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonalds formula for R0 and its entomological derivative, vectorial capacity, are now used to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context for mosquito blood feeding, the movement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Human Movement Data for Malaria Control and Elimination Strategic Planning

Recent increases in funding for malaria control have led to the reduction in transmission in many malaria endemic countries, prompting the national control programmes of 36 malaria endemic countries to set elimination targets. Accounting for human population movement (HPM) in planning for control, elimination and post-elimination surveillance is important, as evidenced by previous elimination attempts that were undermined by the reintroduction of malaria through HPM. Strategic control and elimination planning, therefore, requires quantitative information on HPM patterns and the translation of these into parasite dispersion. HPM patterns and the risk of malaria vary substantially across spatial and temporal scales, demographic and socioeconomic sub-groups, and motivation for travel, so multiple data sets are likely required for quantification of movement. While existing studies based on mobile phone call record data combined with malaria transmission maps have begun to address within-country HPM patterns, other aspects remain poorly quantified despite their importance in accurately gauging malaria movement patterns and building control and detection strategies, such as cross-border HPM, demographic and socioeconomic stratification of HPM patterns, forms of transport, personal malaria protection and other factors that modify malaria risk. A wealth of data exist to aid filling these gaps, which, when combined with spatial data on transport infrastructure, traffic and malaria transmission, can answer relevant questions to guide strategic planning. This review aims to (i) discuss relevant types of HPM across spatial and temporal scales, (ii) document where datasets exist to quantify HPM, (iii) highlight where data gaps remain and (iv) briefly put forward methods for integrating these datasets in a Geographic Information System (GIS) framework for analysing and modelling human population and Plasmodium falciparum malaria infection movements.

The use of census migration data to approximate human movement patterns across temporal scales

Human movement plays a key role in economies and development, the delivery of services, and the spread of infectious diseases. However, it remains poorly quantified partly because reliable data are often lacking, particularly for low-income countries. The most widely available are migration data from human population censuses, which provide valuable information on relatively long timescale relocations across countries, but do not capture the shorter-scale patterns, trips less than a year, that make up the bulk of human movement. Census-derived migration data may provide valuable proxies for shorter-term movements however, as substantial migration between regions can be indicative of well connected places exhibiting high levels of movement at finer time scales, but this has never been examined in detail. Here, an extensive mobile phone usage data set for Kenya was processed to extract movements between counties in 2009 on weekly, monthly, and annual time scales and compared to data on change in residence from the national census conducted during the same time period. We find that the relative ordering across Kenyan counties for incoming, outgoing and between-county movements shows strong correlations. Moreover, the distributions of trip durations from both sources of data are similar, and a spatial interaction model fit to the data reveals the relationships of different parameters over a range of movement time scales. Significant relationships between census migration data and fine temporal scale movement patterns exist, and results suggest that census data can be used to approximate certain features of movement patterns across multiple temporal scales, extending the utility of census-derived migration data.

Parameterization and sensitivity analysis of a complex simulation model for mosquito population dynamics, dengue transmission, and their control.

Models can be useful tools for understanding the dynamics and control of mosquito-borne disease. More detailed models may be more realistic and better suited for understanding local disease dynamics; however, evaluating model suitability, accuracy, and performance becomes increasingly difficult with greater model complexity. Sensitivity analysis is a technique that permits exploration of complex models by evaluating the sensitivity of the model to changes in parameters. Here, we present results of sensitivity analyses of two interrelated complex simulation models of mosquito population dynamics and dengue transmission. We found that dengue transmission may be influenced most by survival in each life stage of the mosquito, mosquito biting behavior, and duration of the infectious period in humans. The importance of these biological processes for vector-borne disease models and the overwhelming lack of knowledge about them make acquisition of relevant field data on these biological processes a top research priority.

Millennium development health metrics: where do Africa's children and women of childbearing age live?

The Millennium Development Goals (MDGs) have prompted an expansion in approaches to deriving health metrics to measure progress toward their achievement. Accurate measurements should take into account the high degrees of spatial heterogeneity in health risks across countries, and this has prompted the development of sophisticated cartographic techniques for mapping and modeling risks. Conversion of these risks to relevant population-based metrics requires equally detailed information on the spatial distribution and attributes of the denominator populations. However, spatial information on age and sex composition over large areas is lacking, prompting many influential studies that have rigorously accounted for health risk heterogeneities to overlook the substantial demographic variations that exist subnationally and merely apply national-level adjustments.Here we outline the development of high resolution age- and sex-structured spatial population datasets for Africa in 2000-2015 built from over a million measurements from more than 20,000 subnational units, increasing input data detail from previous studies by over 400-fold. We analyze the large spatial variations seen within countries and across the continent for key MDG indicator groups, focusing on children under 5 and women of childbearing age, and find that substantial differences in health and development indicators can result through using only national level statistics, compared to accounting for subnational variation.Progress toward meeting the MDGs will be measured through national-level indicators that mask substantial inequalities and heterogeneities across nations. Cartographic approaches are providing opportunities for quantitative assessments of these inequalities and the targeting of interventions, but demographic spatial datasets to support such efforts remain reliant on coarse and outdated input data for accurately locating risk groups. We have shown here that sufficient data exist to map the distribution of key vulnerable groups, and that doing so has substantial impacts on derived metrics through accounting for spatial demographic heterogeneities that exist within nations across Africa.

Theory and data for simulating fine-scale human movement in an urban environment

Individual-based models of infectious disease transmission depend on accurate quantification of fine-scale patterns of human movement. Existing models of movement either pertain to overly coarse scales, simulate some aspects of movement but not others, or were designed specifically for populations in developed countries. Here, we propose a generalizable framework for simulating the locations that an individual visits, time allocation across those locations, and population-level variation therein. As a case study, we fit alternative models for each of five aspects of movement (number, distance from home and types of locations visited; frequency and duration of visits) to interview data from 157 residents of the city of Iquitos, Peru. Comparison of alternative models showed that location type and distance from home were significant determinants of the locations that individuals visited and how much time they spent there. We also found that for most locations, residents of two neighbourhoods displayed indistinguishable preferences for visiting locations at various distances, despite differing distributions of locations around those neighbourhoods. Finally, simulated patterns of time allocation matched the interview data in a number of ways, suggesting that our framework constitutes a sound basis for simulating fine-scale movement and for investigating factors that influence it.

Quantifying cross-border movements and migrations for guiding the strategic planning of malaria control and elimination

BackgroundIdentifying human and malaria parasite movements is important for control planning across all transmission intensities. Imported infections can reintroduce infections into areas previously free of infection, maintain ‘hotspots’ of transmission and import drug resistant strains, challenging national control programmes at a variety of temporal and spatial scales. Recent analyses based on mobile phone usage data have provided valuable insights into population and likely parasite movements within countries, but these data are restricted to sub-national analyses, leaving important cross-border movements neglected.MethodsNational census data were used to analyse and model cross-border migration and movement, using East Africa as an example. ‘Hotspots’ of origin-specific immigrants from neighbouring countries were identified for Kenya, Tanzania and Uganda. Populations of origin-specific migrants were compared to distance from origin country borders and population size at destination, and regression models were developed to quantify and compare differences in migration patterns. Migration data were then combined with existing spatially-referenced malaria data to compare the relative propensity for cross-border malaria movement in the region.ResultsThe spatial patterns and processes for immigration were different between each origin and destination country pair. Hotspots of immigration, for example, were concentrated close to origin country borders for most immigrants to Tanzania, but for Kenya, a similar pattern was only seen for Tanzanian and Ugandan immigrants. Regression model fits also differed between specific migrant groups, with some migration patterns more dependent on population size at destination and distance travelled than others. With these differences between immigration patterns and processes, and heterogeneous transmission risk in East Africa and the surrounding region, propensities to import malaria infections also likely show substantial variations.ConclusionThis was a first attempt to quantify and model cross-border movements relevant to malaria transmission and control. With national census available worldwide, this approach can be translated to construct a cross-border human and malaria movement evidence base for other malaria endemic countries. The outcomes of this study will feed into wider efforts to quantify and model human and malaria movements in endemic regions to facilitate improved intervention planning, resource allocation and collaborative policy decisions.

An Open-Access Modeled Passenger Flow Matrix for the Global Air Network in 2010

The expanding global air network provides rapid and wide-reaching connections accelerating both domestic and international travel. To understand human movement patterns on the network and their socioeconomic, environmental and epidemiological implications, information on passenger flow is required. However, comprehensive data on global passenger flow remain difficult and expensive to obtain, prompting researchers to rely on scheduled flight seat capacity data or simple models of flow. This study describes the construction of an open-access modeled passenger flow matrix for all airports with a host city-population of more than 100,000 and within two transfers of air travel from various publicly available air travel datasets. Data on network characteristics, city population, and local area GDP amongst others are utilized as covariates in a spatial interaction framework to predict the air transportation flows between airports. Training datasets based on information from various transportation organizations in the United States, Canada and the European Union were assembled. A log-linear model controlling the random effects on origin, destination and the airport hierarchy was then built to predict passenger flows on the network, and compared to the results produced using previously published models. Validation analyses showed that the model presented here produced improved predictive power and accuracy compared to previously published models, yielding the highest successful prediction rate at the global scale. Based on this model, passenger flows between 1,491 airports on 644,406 unique routes were estimated in the prediction dataset. The airport node characteristics and estimated passenger flows are freely available as part of the Vector-Borne Disease Airline Importation Risk (VBD-Air) project at: www.vbd-air.com/data.

Mapping internal connectivity through human migration in malaria endemic countries.

Human mobility continues to increase in terms of volumes and reach, producing growing global connectivity. This connectivity hampers efforts to eliminate infectious diseases such as malaria through reintroductions of pathogens, and thus accounting for it becomes important in designing global, continental, regional, and national strategies. Recent works have shown that census-derived migration data provides a good proxy for internal connectivity, in terms of relative strengths of movement between administrative units, across temporal scales. To support global malaria eradication strategy efforts, here we describe the construction of an open access archive of estimated internal migration flows in endemic countries built through pooling of census microdata. These connectivity datasets, described here along with the approaches and methods used to create and validate them, are available both through the WorldPop website and the WorldPop Dataverse Repository.