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Kalthof MWML, Gravey M, Wijnands F, Karssenberg D. Predicting Continental Scale Malaria With Land Surface Water Predictors Based on Malaria Dispersal Mechanisms and High-Resolution Earth Observation Data. GEOHEALTH 2023; 7:e2023GH000811. [PMID: 37822333 PMCID: PMC10564405 DOI: 10.1029/2023gh000811] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/27/2023] [Revised: 08/24/2023] [Accepted: 08/28/2023] [Indexed: 10/13/2023]
Abstract
Despite malaria prevalence being linked to surface water through vector breeding, spatial malaria predictors representing surface water often predict malaria poorly. Furthermore, precipitation, which precursors surface water, often performs better. Our goal is to determine whether novel surface water exposure indices that take malaria dispersal mechanisms into account, derived from new high-resolution surface water data, can be stronger predictors of malaria prevalence compared to precipitation. One hundred eighty candidate predictors were created by combining three surface water malaria exposures from high-accuracy and resolution (5 m resolution, overall accuracy 96%, Kappa Coefficient 0.89, Commission and Omission error 3% and 13%, respectively) water maps of East Africa. Through variable contribution analysis a subset of strong predictors was selected and used as input for Boosted Regression Tree models. We benchmarked the performance and Relative Contribution of this set of novel predictors to models using precipitation instead of surface water predictors, alternative lower resolution predictors, and simpler surface water predictors used in previous studies. The predictive performance of the novel indices rivaled or surpassed that of precipitation predictors. The novel indices substantially improved performance over the identical set of predictors derived from the lower resolution Joint Research Center surface water data set (+10% R 2, +17% Relative Contribution) and over the set of simpler predictors (+18% R 2, +30% Relative Contribution). Surface water derived indices can be strong predictors of malaria, if the spatial resolution is sufficiently high to detect small waterbodies and dispersal mechanisms of malaria related to surface water in human and vector water exposure assessment are incorporated.
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Affiliation(s)
- Maurice W. M. L. Kalthof
- Institute for Environmental Studies (IVM)Vrije Universiteit AmsterdamAmsterdamThe Netherlands
- Department of Physical GeographyUtrecht UniversityUtrechtThe Netherlands
| | - Mathieu Gravey
- Institute for Interdisciplinary Mountain ResearchÖsterreichische Akademie der WissenschaftenInnsbruckAustria
| | - Flore Wijnands
- Institutionen för Geologiska VetenskaperStockholm UniversityStockholmSweden
| | - Derek Karssenberg
- Department of Physical GeographyUtrecht UniversityUtrechtThe Netherlands
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Wu SL, Henry JM, Citron DT, Mbabazi Ssebuliba D, Nakakawa Nsumba J, Sánchez C HM, Brady OJ, Guerra CA, García GA, Carter AR, Ferguson HM, Afolabi BE, Hay SI, Reiner RC, Kiware S, Smith DL. Spatial dynamics of malaria transmission. PLoS Comput Biol 2023; 19:e1010684. [PMID: 37307282 DOI: 10.1371/journal.pcbi.1010684] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2022] [Accepted: 05/15/2023] [Indexed: 06/14/2023] Open
Abstract
The Ross-Macdonald model has exerted enormous influence over the study of malaria transmission dynamics and control, but it lacked features to describe parasite dispersal, travel, and other important aspects of heterogeneous transmission. Here, we present a patch-based differential equation modeling framework that extends the Ross-Macdonald model with sufficient skill and complexity to support planning, monitoring and evaluation for Plasmodium falciparum malaria control. We designed a generic interface for building structured, spatial models of malaria transmission based on a new algorithm for mosquito blood feeding. We developed new algorithms to simulate adult mosquito demography, dispersal, and egg laying in response to resource availability. The core dynamical components describing mosquito ecology and malaria transmission were decomposed, redesigned and reassembled into a modular framework. Structural elements in the framework-human population strata, patches, and aquatic habitats-interact through a flexible design that facilitates construction of ensembles of models with scalable complexity to support robust analytics for malaria policy and adaptive malaria control. We propose updated definitions for the human biting rate and entomological inoculation rates. We present new formulas to describe parasite dispersal and spatial dynamics under steady state conditions, including the human biting rates, parasite dispersal, the "vectorial capacity matrix," a human transmitting capacity distribution matrix, and threshold conditions. An [Formula: see text] package that implements the framework, solves the differential equations, and computes spatial metrics for models developed in this framework has been developed. Development of the model and metrics have focused on malaria, but since the framework is modular, the same ideas and software can be applied to other mosquito-borne pathogen systems.
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Affiliation(s)
- Sean L Wu
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
| | - John M Henry
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
- Quantitative Ecology and Resource Management, University of Washington, Seattle, Washington, United States of America
| | - Daniel T Citron
- Department of Population Health, Grossman School of Medicine, New York University, New York, New York, United States of America
| | | | - Juliet Nakakawa Nsumba
- Department of Mathematics, Makerere University Department of Mathematics, School of Physical Sciences, College of Natural Science, Makerere University, Kampala, Uganda
| | - Héctor M Sánchez C
- Division of Epidemiology, School of Public Health, University of California Berkeley, Berkeley, California, United States of America
- Division of Biostatistics, School of Public Health, University of California Berkeley, Berkeley, California, United States of America
| | - Oliver J Brady
- Centre for Mathematical Modelling of Infectious Diseases, London School of Hygiene & Tropical Medicine, London, United Kingdom
- Department of Infectious Disease Epidemiology, Faculty of Epidemiology and Population Health, London School of Hygiene & Tropical Medicine, London, United Kingdom
| | - Carlos A Guerra
- MCD Global Health, Silver Spring, Maryland, United States of America
| | | | - Austin R Carter
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
| | - Heather M Ferguson
- Faculty of Biomedical and Life Sciences, University of Glasgow, Glasgow, Scotland, United Kingdom
| | - Bakare Emmanuel Afolabi
- International Centre for Applied Mathematical Modelling and Data Analytics, Federal University Oye Ekiti, Ekiti State, Nigeria
- Department of Mathematics, Federal University Oye Ekiti, Ekiti State, Nigeria
| | - Simon I Hay
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
- Department of Health Metrics Science, University of Washington, Seattle, Washington, United States of America
| | - Robert C Reiner
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
- Department of Health Metrics Science, University of Washington, Seattle, Washington, United States of America
| | - Samson Kiware
- Ifakara Health Institute, Dar es Salaam, Tanzania
- Pan-African Mosquito Control Association (PAMCA), Nairobi, Kenya
| | - David L Smith
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, Washington, United States of America
- Department of Health Metrics Science, University of Washington, Seattle, Washington, United States of America
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Saucedo O, Tien JH. Host movement, transmission hot spots, and vector-borne disease dynamics on spatial networks. Infect Dis Model 2022; 7:742-760. [DOI: 10.1016/j.idm.2022.10.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2022] [Revised: 09/04/2022] [Accepted: 10/26/2022] [Indexed: 11/06/2022] Open
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Omitting age-dependent mosquito mortality in malaria models underestimates the effectiveness of insecticide-treated nets. PLoS Comput Biol 2022; 18:e1009540. [PMID: 36121847 PMCID: PMC9522293 DOI: 10.1371/journal.pcbi.1009540] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/07/2021] [Revised: 09/29/2022] [Accepted: 08/08/2022] [Indexed: 11/19/2022] Open
Abstract
Mathematical models of vector-borne infections, including malaria, often assume age-independent mortality rates of vectors, despite evidence that many insects senesce. In this study we present survival data on insecticide-resistant Anopheles gambiae s.l. from experiments in Côte d’Ivoire. We fit a constant mortality function and two age-dependent functions (logistic and Gompertz) to the data from mosquitoes exposed (treated) and not exposed (control) to insecticide-treated nets (ITNs), to establish biologically realistic survival functions. This enables us to explore the effects of insecticide exposure on mosquito mortality rates, and the extent to which insecticide resistance might impact the effectiveness of ITNs. We investigate this by calculating the expected number of infectious bites a mosquito will take in its lifetime, and by extension the vectorial capacity. Our results show that the predicted vectorial capacity is substantially lower in mosquitoes exposed to ITNs, despite the mosquitoes in the experiment being highly insecticide-resistant. The more realistic age-dependent functions provide a better fit to the experimental data compared to a constant mortality function and, hence, influence the predicted impact of ITNs on malaria transmission potential. In models with age-independent mortality, there is a great reduction for the vectorial capacity under exposure compared to no exposure. However, the two age-dependent functions predicted an even larger reduction due to exposure, highlighting the impact of incorporating age in the mortality rates. These results further show that multiple exposures to ITNs had a considerable effect on the vectorial capacity. Overall, the study highlights the importance of including age dependency in mathematical models of vector-borne disease transmission and in fully understanding the impact of interventions. Interventions against malaria are most commonly targeted on the adult mosquitoes, which transmit the infection from person to person. One of the most important interventions are bed-nets, treated with insecticides. Unfortunately, extensive exposure of mosquitoes to insecticide has led to widespread evolution of insecticide resistance, which might threaten control strategies. Piecing together the overall impact of resistance on the efficacy of insecticide-treated nets is complex, but can be informed by the use of mathematical models. However, there are some assumptions that the models frequently use which are not realistic in terms of the mosquito biology. In this paper, we formulate a model that includes age-dependent mortality rates, an important parameter in vector control since control strategies most commonly aim to reduce the lifespan of the mosquitoes. By using novel data collected using field-derived insecticide-resistant mosquitoes, we explore the effects that the presence of insecticides on nets have on the mortality rates, as well as the difference incorporating age dependency in the model has on the results. We find that including age-dependent mortality greatly alters the anticipated effects of insecticide-treated nets on mosquito transmission potential, and that ignoring this realism potentially overestimates the negative impact of insecticide resistance.
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Vargas Bernal E, Saucedo O, Tien JH. Relating Eulerian and Lagrangian spatial models for vector-host disease dynamics through a fundamental matrix. J Math Biol 2022; 84:57. [PMID: 35676373 DOI: 10.1007/s00285-022-01761-z] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2021] [Revised: 01/21/2022] [Accepted: 05/11/2022] [Indexed: 11/26/2022]
Abstract
We explore the relationship between Eulerian and Lagrangian approaches for modeling movement in vector-borne diseases for discrete space. In the Eulerian approach we account for the movement of hosts explicitly through movement rates captured by a graph Laplacian matrix L. In the Lagrangian approach we only account for the proportion of time that individuals spend in foreign patches through a mixing matrix P. We establish a relationship between an Eulerian model and a Lagrangian model for the hosts in terms of the matrices L and P. We say that the two modeling frameworks are consistent if for a given matrix P, the matrix L can be chosen so that the residence times of the matrix P and the matrix L match. We find a sufficient condition for consistency, and examine disease quantities such as the final outbreak size and basic reproduction number in both the consistent and inconsistent cases. In the special case of a two-patch model, we observe how similar values for the basic reproduction number and final outbreak size can occur even in the inconsistent case. However, there are scenarios where the final sizes in both approaches can significantly differ by means of the relationship we propose.
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Affiliation(s)
| | - Omar Saucedo
- Department of Mathematics, Virginia Tech., Blacksburg, VA, USA
| | - Joseph Hua Tien
- Department of Mathematics, The Ohio State University, Columbus, OH, USA
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Mfueni Bikundi E, Coppieters Y. Prediction ability of vector species, environmental characteristics and socio-economic factors for malaria risk in Sub-Saharan African Countries. INTERNATIONAL JOURNAL OF ENVIRONMENTAL HEALTH RESEARCH 2022; 32:191-206. [PMID: 32279543 DOI: 10.1080/09603123.2020.1745763] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/14/2019] [Accepted: 03/18/2020] [Indexed: 06/11/2023]
Abstract
Malaria remains a major public health problem, causing 435,000 deaths in 2017. The objective of this study was to estimate the prediction ability of vector species associated with the prediction power of environmental and socio-economic factors for malaria risk. Logistic regression was used for malaria risk estimation. A Radial Basis Function model was applied for estimating the predictive ability of Anopheles species, environmental and socio-economic factors. The lowest fever prevalence was found where Anopheles melas was dominant. Anopheles coluzzi and Anopheles gambiae were the dominant species where prevalence of malaria was high. Altitude, country and vector species were the best predictive factors. Anopheles arabiensis, An. coluzzi and An. gambiae were most common in urban areas. This study will improve the prediction of malaria risk in targeted areas. We have observed how important it is to adapt health policies according to the dominant malaria vector in a region.
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Affiliation(s)
- Elvire Mfueni Bikundi
- Epidemiology, Biostatistics and Clinical Research Center, School of Public Health, Université Libre de Bruxelles (ULB), Campus Erasme, Brussels, Belgium
| | - Yves Coppieters
- Epidemiology, Biostatistics and Clinical Research Center, School of Public Health, Université Libre de Bruxelles (ULB), Campus Erasme, Brussels, Belgium
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Staffini A, Svensson AK, Chung UI, Svensson T. An Agent-Based Model of the Local Spread of SARS-CoV-2: Modeling Study. JMIR Med Inform 2021; 9:e24192. [PMID: 33750735 PMCID: PMC8025915 DOI: 10.2196/24192] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2020] [Revised: 11/06/2020] [Accepted: 03/21/2021] [Indexed: 01/29/2023] Open
Abstract
BACKGROUND The spread of SARS-CoV-2, originating in Wuhan, China, was classified as a pandemic by the World Health Organization on March 11, 2020. The governments of affected countries have implemented various measures to limit the spread of the virus. The starting point of this paper is the different government approaches, in terms of promulgating new legislative regulations to limit the virus diffusion and to contain negative effects on the populations. OBJECTIVE This paper aims to study how the spread of SARS-CoV-2 is linked to government policies and to analyze how different policies have produced different results on public health. METHODS Considering the official data provided by 4 countries (Italy, Germany, Sweden, and Brazil) and from the measures implemented by each government, we built an agent-based model to study the effects that these measures will have over time on different variables such as the total number of COVID-19 cases, intensive care unit (ICU) bed occupancy rates, and recovery and case-fatality rates. The model we implemented provides the possibility of modifying some starting variables, and it was thus possible to study the effects that some policies (eg, keeping the national borders closed or increasing the ICU beds) would have had on the spread of the infection. RESULTS The 4 considered countries have adopted different containment measures for COVID-19, and the forecasts provided by the model for the considered variables have given different results. Italy and Germany seem to be able to limit the spread of the infection and any eventual second wave, while Sweden and Brazil do not seem to have the situation under control. This situation is also reflected in the forecasts of pressure on the National Health Services, which see Sweden and Brazil with a high occupancy rate of ICU beds in the coming months, with a consequent high number of deaths. CONCLUSIONS In line with what we expected, the obtained results showed that the countries that have taken restrictive measures in terms of limiting the population mobility have managed more successfully than others to contain the spread of COVID-19. Moreover, the model demonstrated that herd immunity cannot be reached even in countries that have relied on a strategy without strict containment measures.
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Affiliation(s)
- Alessio Staffini
- Department of Economics and Finance, Catholic University of Milan, Milan, Italy
- Project Promotion Department, ALBERT Inc, Tokyo, Japan
- Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
| | - Akiko Kishi Svensson
- Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Department of Clinical Sciences, Lund University, Malmö, Sweden
- Department of Diabetes and Metabolic Diseases, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
| | - Ung-Il Chung
- Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- School of Health Innovation, Kanagawa University of Human Services, Tonomachi, Japan
- Clinical Biotechnology, Center for Disease Biology and Integrative Medicine, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
| | - Thomas Svensson
- Precision Health, Department of Bioengineering, Graduate School of Engineering, The University of Tokyo, Tokyo, Japan
- Department of Clinical Sciences, Lund University, Malmö, Sweden
- School of Health Innovation, Kanagawa University of Human Services, Tonomachi, Japan
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Villa M, Buysse M, Berthomieu A, Rivero A. The transmission-blocking effects of antimalarial drugs revisited: fitness costs and sporontocidal effects of artesunate and sulfadoxine-pyrimethamine. Int J Parasitol 2021; 51:279-289. [PMID: 33508331 DOI: 10.1016/j.ijpara.2020.09.012] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2020] [Revised: 09/22/2020] [Accepted: 09/23/2020] [Indexed: 12/31/2022]
Abstract
Assays used to evaluate the transmission-blocking activity of antimalarial drugs are largely focused on their potential to inhibit or reduce the infectivity of gametocytes, the blood stages of the parasite that are responsible for the onward transmission to the mosquito vector. For this purpose, the drug is administered concomitantly with gametocyte-infected blood, and the results are evaluated as the percentage of reduction in the number of oocysts in the mosquito midgut. We report the results of a series of experiments that explore the transmission-blocking potential of two key antimalarial drugs, artesunate and sulfadoxine-pyrimethamine, when administered to mosquitoes already infected from a previous blood meal. For this purpose, uninfected mosquitoes and mosquitoes carrying a 6 day old Plasmodium relictum infection (early oocyst stages) were allowed to feed either on a drug-treated or an untreated host in a fully factorial experiment. This protocol allowed us to bypass the gametocyte stages and establish whether the drugs have a sporontocidal effect, i.e. whether they are able to arrest the ongoing development of oocysts and sporozoites, as would be the case when a mosquito takes a post-infection treated blood meal. In a separate experiment, we also explored whether a drug-treated blood meal impacted key life history traits of the mosquito relevant for transmission, and if this depended on their infection status. Our results showed that feeding on an artesunate- or sulfadoxine-pyrimethamine-treated hosts has no epidemiologically relevant effects on the fitness of infected or uninfected mosquitoes. In contrast, when infected mosquitoes fed on an sulfadoxine-pyrimethamine-treated host, we observed both a significant increase in the number of oocysts in the midgut, and a drastic decrease in both sporozoite prevalence (-30%) and burden (-80%) compared with the untreated controls. We discuss the potential mechanisms underlying these seemingly contradictory results and contend that, provided the results are translatable to human malaria, the potential epidemiological and evolutionary consequences of the current preventive use of sulfadoxine-pyrimethamine in malaria-endemic countries could be substantial.
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Affiliation(s)
- M Villa
- MIVEGEC (CNRS - IRD - Université de Montpellier), France.
| | - M Buysse
- MIVEGEC (CNRS - IRD - Université de Montpellier), France
| | - A Berthomieu
- MIVEGEC (CNRS - IRD - Université de Montpellier), France; CREES (Centre d'Écologie et Évolution de la Santé, Montpellier), 911 avenue Agropolis, 34394 Montpellier, France
| | - A Rivero
- MIVEGEC (CNRS - IRD - Université de Montpellier), France; CREES (Centre d'Écologie et Évolution de la Santé, Montpellier), 911 avenue Agropolis, 34394 Montpellier, France
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9
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Endo N, Eltahir EAB. Prevention of malaria transmission around reservoirs: an observational and modelling study on the effect of wind direction and village location. Lancet Planet Health 2018; 2:e406-e413. [PMID: 30177009 DOI: 10.1016/s2542-5196(18)30175-x] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2017] [Revised: 07/19/2018] [Accepted: 07/20/2018] [Indexed: 06/08/2023]
Abstract
BACKGROUND Many large dams are constructed annually in Africa, with associated reservoirs that might exacerbate the risk of malaria in new villages built nearby. We aimed to investigate the heterogeneous risk of malaria around reservoirs related to the impact of wind direction on malaria transmission. METHODS Between June 15, 2012, and April 22, 2015, we obtained field data on climate and hydrological conditions, and monitored Anopheles mosquito populations around the Koka reservoir in Ethiopia using in-situ weather stations, mosquito light traps, and larval dipping. The field data were used to calibrate a field-tested, spatially explicit mechanistic malaria transmission model, the Hydrology, Entomology, and Malaria Transmission Simulator (HYDREMATS), to investigate the effect of relative wind direction on malaria transmission and associated mechanisms. We combined our simulation results and observational data to assess the association between village location around a reservoir and risk of malaria. FINDINGS HYDREMATS simulations showed that wind blowing from a village towards a reservoir increases the size of malaria vector populations, whereas wind blowing from a reservoir towards a village decreases the size of malaria vector populations, which was consistent with our field data. Larval mortality is low in locations with village-to-reservoir wind due to weak surface waves, and this wind direction creates conditions that enable mosquitoes to identify village locations more easily than in conditions caused by reservoir-to-village wind, which increases the size of malaria vector populations, and thus malaria transmission. Among the wind conditions investigated (0·5-5 m/s), the effect of CO2 attraction on the size of the Anopheles population was largest at wind speeds of 0·5 m/s and 1 m/s, decreasing with higher wind speed. At a wind speed of 5 m/s, the effect of CO2 attraction was negligible, whereas the effect of waves was strongest. The effect of advection on Anopheles population size was negligible at all wind speeds and wind directions. INTERPRETATION The effect of wind on malaria transmission around reservoirs can be substantial. The transmission of malaria can be minimised if the location of villages situated near a reservoir is carefully considered. For areas in which the environmental conditions surrounding a resevoir are equal, villages should be located downwind of reservoirs to reduce the incidence of malaria, although further research will be required in locations where wind direction changes in different seasons. FUNDING US National Science Foundation, and Cooperative Agreement between the Masdar Institute of Science and Technology, Abu Dhabi, UAE, and the Massachusetts Institute of Technology, Cambridge, MA, USA.
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Affiliation(s)
- Noriko Endo
- Ralph M Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
| | - Elfatih A B Eltahir
- Ralph M Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA
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Smith NR, Trauer JM, Gambhir M, Richards JS, Maude RJ, Keith JM, Flegg JA. Agent-based models of malaria transmission: a systematic review. Malar J 2018; 17:299. [PMID: 30119664 PMCID: PMC6098619 DOI: 10.1186/s12936-018-2442-y] [Citation(s) in RCA: 43] [Impact Index Per Article: 7.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/21/2018] [Accepted: 08/04/2018] [Indexed: 01/20/2023] Open
Abstract
BACKGROUND Much of the extensive research regarding transmission of malaria is underpinned by mathematical modelling. Compartmental models, which focus on interactions and transitions between population strata, have been a mainstay of such modelling for more than a century. However, modellers are increasingly adopting agent-based approaches, which model hosts, vectors and/or their interactions on an individual level. One reason for the increasing popularity of such models is their potential to provide enhanced realism by allowing system-level behaviours to emerge as a consequence of accumulated individual-level interactions, as occurs in real populations. METHODS A systematic review of 90 articles published between 1998 and May 2018 was performed, characterizing agent-based models (ABMs) relevant to malaria transmission. The review provides an overview of approaches used to date, determines the advantages of these approaches, and proposes ideas for progressing the field. RESULTS The rationale for ABM use over other modelling approaches centres around three points: the need to accurately represent increased stochasticity in low-transmission settings; the benefits of high-resolution spatial simulations; and heterogeneities in drug and vaccine efficacies due to individual patient characteristics. The success of these approaches provides avenues for further exploration of agent-based techniques for modelling malaria transmission. Potential extensions include varying elimination strategies across spatial landscapes, extending the size of spatial models, incorporating human movement dynamics, and developing increasingly comprehensive parameter estimation and optimization techniques. CONCLUSION Collectively, the literature covers an extensive array of topics, including the full spectrum of transmission and intervention regimes. Bringing these elements together under a common framework may enhance knowledge of, and guide policies towards, malaria elimination. However, because of the diversity of available models, endorsing a standardized approach to ABM implementation may not be possible. Instead it is recommended that model frameworks be contextually appropriate and sufficiently described. One key recommendation is to develop enhanced parameter estimation and optimization techniques. Extensions of current techniques will provide the robust results required to enhance current elimination efforts.
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Affiliation(s)
- Neal R Smith
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia.
| | - James M Trauer
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
| | - Manoj Gambhir
- School of Public Health and Preventive Medicine, Monash University, Melbourne, Australia
- IBM Research Australia, Melbourne, Australia
| | - Jack S Richards
- Life Sciences, Burnet Institute, Melbourne, Australia
- Department of Medicine, University of Melbourne, Parkville, Australia
- Department of Infectious Diseases, Monash University, Melbourne, Australia
| | - Richard J Maude
- Mahidol-Oxford Tropical Medicine Research Unit, Faculty of Tropical Medicine, Mahidol University, Bangkok, Thailand
- Centre for Tropical Medicine and Global Health, Nuffield Department of Medicine, University of Oxford, Oxford, UK
- Harvard TH Chan School of Public Health, Harvard University, Boston, USA
| | - Jonathan M Keith
- School of Mathematical Sciences, Monash University, Clayton, Australia
| | - Jennifer A Flegg
- School of Mathematics and Statistics, University of Melbourne, Parkville, Australia
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Pizzitutti F, Pan W, Feingold B, Zaitchik B, Álvarez CA, Mena CF. Out of the net: An agent-based model to study human movements influence on local-scale malaria transmission. PLoS One 2018; 13:e0193493. [PMID: 29509795 PMCID: PMC5839546 DOI: 10.1371/journal.pone.0193493] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2017] [Accepted: 02/12/2018] [Indexed: 01/08/2023] Open
Abstract
Though malaria control initiatives have markedly reduced malaria prevalence in recent decades, global eradication is far from actuality. Recent studies show that environmental and social heterogeneities in low-transmission settings have an increased weight in shaping malaria micro-epidemiology. New integrated and more localized control strategies should be developed and tested. Here we present a set of agent-based models designed to study the influence of local scale human movements on local scale malaria transmission in a typical Amazon environment, where malaria is transmission is low and strongly connected with seasonal riverine flooding. The agent-based simulations show that the overall malaria incidence is essentially not influenced by local scale human movements. In contrast, the locations of malaria high risk spatial hotspots heavily depend on human movements because simulated malaria hotspots are mainly centered on farms, were laborers work during the day. The agent-based models are then used to test the effectiveness of two different malaria control strategies both designed to reduce local scale malaria incidence by targeting hotspots. The first control scenario consists in treat against mosquito bites people that, during the simulation, enter at least once inside hotspots revealed considering the actual sites where human individuals were infected. The second scenario involves the treatment of people entering in hotspots calculated assuming that the infection sites of every infected individual is located in the household where the individual lives. Simulations show that both considered scenarios perform better in controlling malaria than a randomized treatment, although targeting household hotspots shows slightly better performance.
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Affiliation(s)
- Francesco Pizzitutti
- Universidad San Francisco de Quito, Instituto de Geografía, Quito, Ecuador
- Duke University, Duke global Health Institute, Durham, NC, United States of America
| | - William Pan
- Duke University, Duke global Health Institute, Durham, NC, United States of America
| | - Beth Feingold
- SUNY-Albany, School of Public Health, Rensselaer, Albany, NY, United States of America
| | - Ben Zaitchik
- Johns Hopkins University, Morton K. Blaustein Department of Earth & Planetary Sciences, Baltimore, MD, United States of America
| | | | - Carlos F. Mena
- Universidad San Francisco de Quito, Instituto de Geografía, Quito, Ecuador
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12
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Endo N, Eltahir EAB. Environmental Determinants of Malaria Transmission Around the Koka Reservoir in Ethiopia. GEOHEALTH 2018; 2:104-115. [PMID: 32159012 PMCID: PMC7007164 DOI: 10.1002/2017gh000108] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/12/2017] [Revised: 01/25/2018] [Accepted: 01/29/2018] [Indexed: 06/08/2023]
Abstract
New dam construction is known to exacerbate malaria transmission in Africa as the vectors of malaria-Anopheles mosquitoes-use bodies of water as breeding sites. Precise environmental mechanisms of how reservoirs exacerbate malaria transmission are yet to be identified. Understanding of these mechanisms should lead to a better assessment of the impacts of dam construction and to new prevention strategies. Combining extensive multiyear field surveys around the Koka Reservoir in Ethiopia and rigorous model development and simulation studies, environmental mechanisms of malaria transmission around the reservoir were examined. Most comprehensive and detailed malaria transmission model, Hydrology, Entomology, and Malaria Transmission Simulator, was applied to a village adjacent to the reservoir. Significant contributions to the dynamics of malaria transmission are shaped by wind profile, marginal pools, temperature, and shoreline locations. Wind speed and wind direction influence Anopheles populations and malaria transmission during the major and secondary mosquito seasons. During the secondary mosquito season, a noticeable influence was also attributed to marginal pools. Temperature was found to play an important role, not so much in Anopheles population dynamics, but in malaria transmission dynamics. Change in shoreline locations drives malaria transmission dynamics, with closer shoreline locations to the village making malaria transmission more likely. Identified environmental mechanisms help in predicting malaria transmission seasons and in developing village relocation strategies upon dam construction to minimize the risk of malaria.
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Affiliation(s)
- Noriko Endo
- Ralph M. Parsons Laboratory, Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeMAUSA
| | - Elfatih A. B. Eltahir
- Ralph M. Parsons Laboratory, Department of Civil and Environmental EngineeringMassachusetts Institute of TechnologyCambridgeMAUSA
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Xu Z, Glass K, Lau CL, Geard N, Graves P, Clements A. A Synthetic Population for Modelling the Dynamics of Infectious Disease Transmission in American Samoa. Sci Rep 2017; 7:16725. [PMID: 29196679 PMCID: PMC5711879 DOI: 10.1038/s41598-017-17093-8] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/08/2017] [Accepted: 11/20/2017] [Indexed: 11/09/2022] Open
Abstract
Agent-based modelling is a useful approach for capturing heterogeneity in disease transmission. In this study, a synthetic population was developed for American Samoa using an iterative approach based on population census, questionnaire survey and land use data. The population will be used as the basis for a new agent-based model, intended specifically to fill the knowledge gaps about lymphatic filariasis transmission and elimination, but also to be readily adaptable to model other infectious diseases. The synthetic population was characterized by the statistically realistic population and household structure, and high-resolution geographic locations of households. The population was simulated over 40 years from 2010 to 2050. The simulated population was compared to estimates and projections of the U.S. Census Bureau. The results showed the total population would continuously decrease due to the observed large number of emigrants. Population ageing was observed, which was consistent with the latest two population censuses and the Bureau's projections. The sex ratios by age groups were analysed and indicated an increase in the proportion of males in age groups 0-14 and 15-64. The household size followed a Gaussian distribution with an average size of around 5.0 throughout the simulation, slightly less than the initial average size 5.6.
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Affiliation(s)
- Zhijing Xu
- Research School of Population Health, Australian National University, Canberra, Australia.
| | - Kathryn Glass
- Research School of Population Health, Australian National University, Canberra, Australia
| | - Colleen L Lau
- Research School of Population Health, Australian National University, Canberra, Australia
| | - Nicholas Geard
- School of Computing and Information Systems, University of Melbourne, Melbourne, Australia.,Melbourne School of Population and Global Health, University of Melbourne, Melbourne, Australia
| | - Patricia Graves
- College of Public Health, Medical and Veterinary Sciences, Division of Tropical Health and Medicine, James Cook University, Cairns, Australia
| | - Archie Clements
- Research School of Population Health, Australian National University, Canberra, Australia
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Abstract
This paper summarises key advances and priorities since the 2011 presentation of the Malaria Eradication Research Agenda (malERA), with a focus on the combinations of intervention tools and strategies for elimination and their evaluation using modelling approaches. With an increasing number of countries embarking on malaria elimination programmes, national and local decisions to select combinations of tools and deployment strategies directed at malaria elimination must address rapidly changing transmission patterns across diverse geographic areas. However, not all of these approaches can be systematically evaluated in the field. Thus, there is potential for modelling to investigate appropriate 'packages' of combined interventions that include various forms of vector control, case management, surveillance, and population-based approaches for different settings, particularly at lower transmission levels. Modelling can help prioritise which intervention packages should be tested in field studies, suggest which intervention package should be used at a particular level or stratum of transmission intensity, estimate the risk of resurgence when scaling down specific interventions after local transmission is interrupted, and evaluate the risk and impact of parasite drug resistance and vector insecticide resistance. However, modelling intervention package deployment against a heterogeneous transmission background is a challenge. Further validation of malaria models should be pursued through an iterative process, whereby field data collected with the deployment of intervention packages is used to refine models and make them progressively more relevant for assessing and predicting elimination outcomes.
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Searle KM, Lubinda J, Hamapumbu H, Shields TM, Curriero FC, Smith DL, Thuma PE, Moss WJ. Characterizing and quantifying human movement patterns using GPS data loggers in an area approaching malaria elimination in rural southern Zambia. ROYAL SOCIETY OPEN SCIENCE 2017; 4:170046. [PMID: 28573009 PMCID: PMC5451810 DOI: 10.1098/rsos.170046] [Citation(s) in RCA: 36] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2017] [Accepted: 04/04/2017] [Indexed: 05/23/2023]
Abstract
In areas approaching malaria elimination, human mobility patterns are important in determining the proportion of malaria cases that are imported or the result of low-level, endemic transmission. A convenience sample of participants enrolled in a longitudinal cohort study in the catchment area of Macha Hospital in Choma District, Southern Province, Zambia, was selected to carry a GPS data logger for one month from October 2013 to August 2014. Density maps and activity space plots were created to evaluate seasonal movement patterns. Time spent outside the household compound during anopheline biting times, and time spent in malaria high- and low-risk areas, were calculated. There was evidence of seasonal movement patterns, with increased long-distance movement during the dry season. A median of 10.6% (interquartile range (IQR): 5.8-23.8) of time was spent away from the household, which decreased during anopheline biting times to 5.6% (IQR: 1.7-14.9). The per cent of time spent in malaria high-risk areas for participants residing in high-risk areas ranged from 83.2% to 100%, but ranged from only 0.0% to 36.7% for participants residing in low-risk areas. Interventions targeted at the household may be more effective because of restricted movement during the rainy season, with limited movement between high- and low-risk areas.
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Affiliation(s)
- Kelly M. Searle
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA
- Author for correspondence: Kelly M. Searle e-mail:
| | | | | | - Timothy M. Shields
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA
| | - Frank C. Curriero
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA
| | - David L. Smith
- Institute for Health Metrics and Evaluation, University of Washington, Seattle, WA, USA
| | | | - William J. Moss
- Department of Epidemiology, Bloomberg School of Public Health, Johns Hopkins University, Baltimore, MD, USA
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Endo N, Eltahir EAB. Environmental determinants of malaria transmission in African villages. Malar J 2016; 15:578. [PMID: 27903266 PMCID: PMC5131557 DOI: 10.1186/s12936-016-1633-7] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/06/2016] [Accepted: 11/23/2016] [Indexed: 12/02/2022] Open
Abstract
Background Malaria transmission is complex, involving a range of hydroclimatological, biological, and environmental processes. The high degree of non-linearity in these processes makes it difficult to predict and intervene against malaria. This study seeks both to define a minimal number of malaria transmission determinants, and to provide a theoretical basis for sustainable environmental manipulation to prevent malaria transmission. Methods Using a field-tested mechanistic malaria model, HYDREMATS, a theoretical study was conducted under hypothetical conditions. Simulations were conducted with a range of hydroclimatological and environmental conditions: temperature (t), length of wet season (Twet), storm inter-arrival time (Tint), persistence of vector breeding pools (Ton), and distribution of houses from breeding pools and from each other (Xdist and Ydist, respectively). Based on the theoretical study, a malaria time scale, To, and a predictive theory of malaria transmission were introduced. The performance of the predictive theory was compared against the observational malaria transmission data in West Africa. Population density was used to estimate the scale that describes the spatial distribution of houses. Results The predictive theory shows a universality in malaria endemic conditions when plotted using two newly-introduced dimension-less parameters. The projected malaria transmission potential compared well with the observation data, and the apparent differences were discussed. The results illustrate the importance of spatial aspects in malaria transmission. Conclusions The predictive theory is useful in measuring malaria transmission potential, and it can also provide guidelines on how to plan the layout of human habitats in order to prevent endemic malaria. Malaria-resistant villages can be designed by locating houses further than critical distances away from breeding pools or by removing pools within a critical distance from houses; the critical distance is described in the context of local climatology and hydrology. Electronic supplementary material The online version of this article (doi:10.1186/s12936-016-1633-7) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Noriko Endo
- Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA.
| | - Elfatih A B Eltahir
- Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA
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Karl S, White MT, Milne GJ, Gurarie D, Hay SI, Barry AE, Felger I, Mueller I. Spatial Effects on the Multiplicity of Plasmodium falciparum Infections. PLoS One 2016; 11:e0164054. [PMID: 27711149 PMCID: PMC5053403 DOI: 10.1371/journal.pone.0164054] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/05/2016] [Accepted: 09/19/2016] [Indexed: 11/18/2022] Open
Abstract
As malaria is being pushed back on many frontiers and global case numbers are declining, accurate measurement and prediction of transmission becomes increasingly difficult. Low transmission settings are characterised by high levels of spatial heterogeneity, which stands in stark contrast to the widely used assumption of spatially homogeneous transmission used in mathematical transmission models for malaria. In the present study an individual-based mathematical malaria transmission model that incorporates multiple parasite clones, variable human exposure and duration of infection, limited mosquito flight distance and most importantly geographically heterogeneous human and mosquito population densities was used to illustrate the differences between homogeneous and heterogeneous transmission assumptions when aiming to predict surrogate indicators of transmission intensity such as population parasite prevalence or multiplicity of infection (MOI). In traditionally highly malaria endemic regions where most of the population harbours malaria parasites, humans are often infected with multiple parasite clones. However, studies have shown also in areas with low overall parasite prevalence, infection with multiple parasite clones is a common occurrence. Mathematical models assuming homogeneous transmission between humans and mosquitoes cannot explain these observations. Heterogeneity of transmission can arise from many factors including acquired immunity, body size and occupational exposure. In this study, we show that spatial heterogeneity has a profound effect on predictions of MOI and parasite prevalence. We illustrate, that models assuming homogeneous transmission underestimate average MOI in low transmission settings when compared to field data and that spatially heterogeneous models predict stable transmission at much lower overall parasite prevalence. Therefore it is very important that models used to guide malaria surveillance and control strategies in low transmission and elimination settings take into account the spatial features of the specific target area, including human and mosquito vector distribution.
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Affiliation(s)
- Stephan Karl
- Population-Based Biology Division, Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- Department of Medical Biology, University of Melbourne, Parkville, Victoria, Australia
- Vector-borne Diseases Unit, Papua New Guinea Insititute of Medical Research, Madang, Madang Province, Papua New Guinea
- * E-mail:
| | - Michael T. White
- Population-Based Biology Division, Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- MRC Centre for Outbreak Analysis & Modelling, Department of Infectious Disease Epidemiology, Imperial College, London, United Kingdom
| | - George J. Milne
- School of Computer Science and Software Engineering, The University of Western Australia, Perth, WA, Australia
| | - David Gurarie
- Department of Mathematics, Applied Mathematics and Statistics, Case Western Reserve University, Cleveland, Ohio, United States of America
| | - Simon I. Hay
- Institute for Health Metrics and Evaluation, Seattle, Washington, United States of America
- Fogarty International Center, National Institutes of Health, Bethesda, Maryland, United States of America
| | - Alyssa E. Barry
- Population-Based Biology Division, Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- Department of Medical Biology, University of Melbourne, Parkville, Victoria, Australia
| | - Ingrid Felger
- Department of Medical Parasitology and Infection Biology Swiss Tropical and Public Health Institute, Basel, Switzerland
- University of Basel, Basel, Switzerland
| | - Ivo Mueller
- Population-Based Biology Division, Walter and Eliza Hall Institute of Medical Research, Parkville, Victoria, Australia
- Department of Medical Biology, University of Melbourne, Parkville, Victoria, Australia
- Malaria: Parasites and Hosts Unit, Department of Parasites & Insect Vectors, Institut Pasteur, Paris, France
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Chung B. Impact of Irrigation Extension on Malaria Transmission in Simret, Tigray, Ethiopia. THE KOREAN JOURNAL OF PARASITOLOGY 2016; 54:399-405. [PMID: 27658590 PMCID: PMC5040095 DOI: 10.3347/kjp.2016.54.4.399] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/06/2016] [Revised: 05/22/2016] [Accepted: 07/09/2016] [Indexed: 11/23/2022]
Abstract
Poor subsistence farmers who live in a semi-arid area of northern Ethiopia build irrigation systems to overcome water shortages. However, there is a high risk of malaria transmission when increased standing water provides more favorable habitats for mosquito breeding. This is a serious problem because there are many barriers to malaria control measures and health care systems in the area. Using a causal loop diagram and computer simulations, the author attempted to visually illustrate positive and negative feedbacks between mosquito and human populations in the context of Simret, which is a small village located in northern Ethiopia and is generally considered a malaria-free area. The simulation results show that the number of infectious mosquitos increases to 17,215 at its peak, accounting for 3.5% of potentially dangerous mosquitos. At the same time, the number of sick people increases to 574 at its peak, accounting for 15% of local population. The malaria outbreak is controlled largely because of a fixed number of vulnerable people or local population that acts as an intermediate host.
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Affiliation(s)
- Bonhee Chung
- Institute for Poverty Alleviation and International Development, Yonsei University, Wonju 26493, Korea
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Pizzitutti F, Pan W, Barbieri A, Miranda JJ, Feingold B, Guedes GR, Alarcon-Valenzuela J, Mena CF. A validated agent-based model to study the spatial and temporal heterogeneities of malaria incidence in the rainforest environment. Malar J 2015; 14:514. [PMID: 26696294 PMCID: PMC4688926 DOI: 10.1186/s12936-015-1030-7] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/09/2015] [Accepted: 12/02/2015] [Indexed: 12/25/2022] Open
Abstract
BACKGROUND The Amazon environment has been exposed in the last decades to radical changes that have been accompanied by a remarkable rise of both Plasmodium falciparum and Plasmodium vivax malaria. The malaria transmission process is highly influenced by factors such as spatial and temporal heterogeneities of the environment and individual-based characteristics of mosquitoes and humans populations. All these determinant factors can be simulated effectively trough agent-based models. METHODS This paper presents a validated agent-based model of local-scale malaria transmission. The model reproduces the environment of a typical riverine village in the northern Peruvian Amazon, where the malaria transmission is highly seasonal and apparently associated with flooding of large areas caused by the neighbouring river. Agents representing humans, mosquitoes and the two species of Plasmodium (P. falciparum and P. vivax) are simulated in a spatially explicit representation of the environment around the village. The model environment includes: climate, people houses positions and elevation. A representation of changes in the mosquito breeding areas extension caused by the river flooding is also included in the simulation environment. RESULTS A calibration process was carried out to reproduce the variations of the malaria monthly incidence over a period of 3 years. The calibrated model is also able to reproduce the spatial heterogeneities of local scale malaria transmission. A "what if" eradication strategy scenario is proposed: if the mosquito breeding sites are eliminated through mosquito larva habitat management in a buffer area extended at least 200 m around the village, the malaria transmission is eradicated from the village. CONCLUSIONS The use of agent-based models can reproduce effectively the spatiotemporal variations of the malaria transmission in a low endemicity environment dominated by river floodings like in the Amazon.
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Affiliation(s)
| | - William Pan
- Duke University, 310 Trent Drive, Room 227, Box 90519, Durham, NC, 27708, USA.
| | - Alisson Barbieri
- Instituto de Geociências-IGC Belo Horizonte, Universidade Federal de Minas Gerais, Belo Horozonte, Brazil.
| | - J Jaime Miranda
- Oswaldo Cruz Foundation (FIOCRUZ), Universidad Peruana Cayetano Heredia, Lima, Peru.
| | - Beth Feingold
- Department of Environmental Health Sciences, School of Public Health, University at Albany, State University of New York, 1 University Place GEC, 145 Rensselaer, New York, NY, 12144, USA.
| | - Gilvan R Guedes
- College of Economics Departamento de Demografia/FACE/UFMG, Office 3093, Av. Antônio Carlos, 6627-Pampulha, Belo Horizonte, Minas Gerais, 31270-901, Brazil.
| | | | - Carlos F Mena
- Universidad San Francisco de Quito, Diego de Robles, s/n, Cumbayá, Ecuador.
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