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Cited by 130Mathematical and Theoretical Epidemiology and Ecology ModelsMosquito-borne diseases and controlMalaria Research and Control

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Heterogeneity, Mixing, and the Spatial Scales of Mosquito-Borne Pathogen Transmission

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Perkins, T. Alex, Scott, Thomas W., Le Menach, Arnaud, Smith, David L.·2013·PLoS Computational Biology
DOI 10.1371/journal.pcbi.1003327PMC PMC3861021
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Abstract

The Ross-Macdonald model has dominated theory for mosquito-borne pathogen transmission dynamics and control for over a century. The model, like many other basic population models, makes the mathematically convenient assumption that populations are well mixed; i.e., that each mosquito is equally likely to bite any vertebrate host. This assumption raises questions about the validity and utility of current theory because it is in conflict with preponderant empirical evidence that transmission is heterogeneous. Here, we propose a new dynamic framework that is realistic enough to describe biological causes of heterogeneous transmission of mosquito-borne pathogens of humans, yet tractable enough to provide a basis for developing and improving general theory. The framework is based on the ecological context of mosquito blood meals and the fine-scale movements of individual mosquitoes and human hosts that give rise to heterogeneous transmission. Using this framework, we describe pathogen dispersion in terms of individual-level analogues of two classical quantities: vectorial capacity and the basic reproductive number, R0. Importantly, this framework explicitly accounts for three key components of overall heterogeneity in transmission: heterogeneous exposure, poor mixing, and finite host numbers. Using these tools, we propose two ways of characterizing the spatial scales of transmission--pathogen dispersion kernels and the evenness of mixing across scales of aggregation--and demonstrate the consequences of a model's choice of spatial scale for epidemic dynamics and for estimation of R0, both by a priori model formulas and by inference of the force of infection from time-series data.

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Figures

Figure 1 Model schematic. The model is specified on a continuous landscape with a point set of blood-feeding habitats, , and a point set of aquatic habitats, . The model is discrete in time with a time step equal to the length of the mosquito feeding cycle, in which mosquitoes take a blood meal, search for aquatic habitat (, red arrow), lay eggs, and repeat the search for another blood meal (, green arrow). Each host in allocates its time proportionally at multiple blood-feeding habitats (, brown arrows). During a single feeding cycle, each mosquito present at a given blood-feeding habitat takes a single blood meal, the collection of which are distributed differentially on hosts according to the proportion of time each spends there and a quantity describing each host's biting suitability (). This model structure allows for the derivation of weighted, bidirectional networks that summarize pathogen dispersion among blood-feeding habitats (houses) or among hosts (circles). From this process-based description of transmission, it is possible to derive network summaries of pathogen dispersion. Pathogen dispersion by mosquitoes: describes how mosquitoes taking an infective blood meal at one blood-feeding habitat distribute secondary, potentially infectious bites at other blood-feeding habitats. Pathogen dispersion by hosts: specifies the probability that a secondary bite on a human infected at one blood-feeding habitat takes place at some other blood-feeding habitat. Pathogen amplification: gives the total number of secondary bites on a host arising from primary bites on another host in a single feeding cycle. Host infection: contains the probabilities that a primary infection in one host will result in a secondary infection in some other host.
Figure 1 Model schematic. The model is specified on a continuous landscape with a point set of blood-feeding habitats, , and a point set of aquatic habitats, . The model is discrete in time with a time step equal to the length of the mosquito feeding cycle, in which mosquitoes take a blood meal, search for aquatic habitat (, red arrow), lay eggs, and repeat the search for another blood meal (, green arrow). Each host in allocates its time proportionally at multiple blood-feeding habitats (, brown arrows). During a single feeding cycle, each mosquito present at a given blood-feeding habitat takes a single blood meal, the collection of which are distributed differentially on hosts according to the proportion of time each spends there and a quantity describing each host's biting suitability (). This model structure allows for the derivation of weighted, bidirectional networks that summarize pathogen dispersion among blood-feeding habitats (houses) or among hosts (circles). From this process-based description of transmission, it is possible to derive network summaries of pathogen dispersion. Pathogen dispersion by mosquitoes: describes how mosquitoes taking an infective blood meal at one blood-feeding habitat distribute secondary, potentially infectious bites at other blood-feeding habitats. Pathogen dispersion by hosts: specifies the probability that a secondary bite on a human infected at one blood-feeding habitat takes place at some other blood-feeding habitat. Pathogen amplification: gives the total number of secondary bites on a host arising from primary bites on another host in a single feeding cycle. Host infection: contains the probabilities that a primary infection in one host will result in a secondary infection in some other host.CC BY · PubMed Central
Figure 2 Spatial kernels. Panels correspond to the matrices that summarize pathogen dispersion by mosquitoes (a), pathogen dispersion by vertebrate hosts (b), pathogen dispersion through both species (c), and the spread of secondary host infections (d). Gray histograms show the empirical densities of each matrix's weighting at different distances, and black curves show a smoothed version of these data. Dashed lines show the average distance at which the events described by each matrix take place and therefore represent one way of defining the spatial scales of transmission with a single number. For example, the dashed line in (d) indicates that, on average, mosquito bites conferring a secondary host infection occur a distance of E away from where the corresponding primary host transmitted the pathogen to a mosquito.
Figure 2 Spatial kernels. Panels correspond to the matrices that summarize pathogen dispersion by mosquitoes (a), pathogen dispersion by vertebrate hosts (b), pathogen dispersion through both species (c), and the spread of secondary host infections (d). Gray histograms show the empirical densities of each matrix's weighting at different distances, and black curves show a smoothed version of these data. Dashed lines show the average distance at which the events described by each matrix take place and therefore represent one way of defining the spatial scales of transmission with a single number. For example, the dashed line in (d) indicates that, on average, mosquito bites conferring a secondary host infection occur a distance of E away from where the corresponding primary host transmitted the pathogen to a mosquito.CC BY · PubMed Central
Figure 3 Mixing across scales. Evenness of mixing of secondary infections within subsets of blood-feeding habitats under different assumptions about their spatial arrangement. Phylograms are structured from bottom (depiction of spatial arrangement of blood feeding habitats) to top (by spatial extent and patch size) such that nearby blood-feeding habitats are grouped together, nearby groups combine to form larger groups, and so on, until all blood-feeding habitats are grouped together. Colors on the branches of the phylograms show the evenness of mixing in the diagonal submatrix of corresponding to blood-feeding habitats that comprise each cluster.
Figure 3 Mixing across scales. Evenness of mixing of secondary infections within subsets of blood-feeding habitats under different assumptions about their spatial arrangement. Phylograms are structured from bottom (depiction of spatial arrangement of blood feeding habitats) to top (by spatial extent and patch size) such that nearby blood-feeding habitats are grouped together, nearby groups combine to form larger groups, and so on, until all blood-feeding habitats are grouped together. Colors on the branches of the phylograms show the evenness of mixing in the diagonal submatrix of corresponding to blood-feeding habitats that comprise each cluster.CC BY · PubMed Central
Figure 4 Heterogeneity across scales. Heterogeneity of outgoing secondary infections from subsets of blood-feeding habitats under different assumptions about their spatial arrangement. Phylograms are structured from bottom (depiction of spatial arrangement of blood feeding habitats) to top (by spatial extent and patch size) such that nearby blood-feeding habitats are grouped together, nearby groups combine to form larger groups, and so on, until all blood-feeding habitats are grouped together. Colors on the branches of the phylograms show the coefficient of variation of the sums across the rows of the diagonal submatrix of corresponding to blood-feeding habitats that comprise each cluster.
Figure 4 Heterogeneity across scales. Heterogeneity of outgoing secondary infections from subsets of blood-feeding habitats under different assumptions about their spatial arrangement. Phylograms are structured from bottom (depiction of spatial arrangement of blood feeding habitats) to top (by spatial extent and patch size) such that nearby blood-feeding habitats are grouped together, nearby groups combine to form larger groups, and so on, until all blood-feeding habitats are grouped together. Colors on the branches of the phylograms show the coefficient of variation of the sums across the rows of the diagonal submatrix of corresponding to blood-feeding habitats that comprise each cluster.CC BY · PubMed Central
Figure 5 Epidemic dynamics across scales. When mosquito and host movement are both well mixed (a), each infectious bite originating from a single primary host is made on a unique secondary host. When mosquito and host movement are both poorly mixed (b), some hosts receive multiple infectious bites. Under these different scenarios about movement, epidemics originating in hosts with equal unfold much differently. Pathogen spread through a well-mixed population is quick, consistent, and complete (red in c), whereas pathogen spread through poorly-mixed populations is slower, more variable, and does not infect the entire host population (blue in c).
Figure 5 Epidemic dynamics across scales. When mosquito and host movement are both well mixed (a), each infectious bite originating from a single primary host is made on a unique secondary host. When mosquito and host movement are both poorly mixed (b), some hosts receive multiple infectious bites. Under these different scenarios about movement, epidemics originating in hosts with equal unfold much differently. Pathogen spread through a well-mixed population is quick, consistent, and complete (red in c), whereas pathogen spread through poorly-mixed populations is slower, more variable, and does not infect the entire host population (blue in c).CC BY · PubMed Central

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Metadata

Authors
Perkins, T. A., Scott, T. W., Le Menach, A., & Smith, D. L.
Affiliations
National Institutes of Health (US)
Corresponding author
Perkins, T. Alex
ORCID
Venue
PLoS Computational Biology
Publisher
Public Library of Science (PLoS)
Published
2013-12-12
Volume
9
Issue
12
Pages
e1003327
ISSN
  • 1553-734X (ISSN-L)
  • 1553-7358
DOI
10.1371/journal.pcbi.1003327
PMC
PMC3861021
OpenAlex
W2072086516
Cited by
130
References
86
Citations by year
2026: 5 · 2025: 8 · 2024: 3 · 2023: 6 · 2022: 6 · 2021: 7 · 2020: 10 · 2019: 9 · 2018: 19 · 2017: 13 · 2016: 16 · 2015: 19 · 2014: 9
FWCI
15.00
Type
journal article
Language
en
Update notices
correction (2014-02-28)
Open access
Licence
Locations
  • PLoS Computational Biology (publishedVersion, cc-by)
  • Europe PMC (PubMed Central) (publishedVersion, cc-by)
  • PubMed Central (publishedVersion, cc-by)
  • PubMed (publishedVersion)
  • RePEc: Research Papers in Economics (submittedVersion)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion, cc-by-sa)
  • eScholarship (California Digital Library) (submittedVersion)
  • eScholarship (California Digital Library) (submittedVersion, cc-by)
Funders
  • U.S. Department of Homeland Security
  • Bill and Melinda Gates Foundation (49446, OPP52250)
  • Bloomberg Family Foundation
  • National Institutes of Health (5r01ai069341-05)
  • National Institute of Allergy and Infectious Diseases (R01-AI069341, U19AI089674)
  • Fogarty International Center
Topics
  • Physical Sciences › Mathematics › Applied Mathematics › Mathematical and Theoretical Epidemiology and Ecology Models
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mosquito-borne diseases and control
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Malaria Research and Control
Keywords
mosquito-borne pathogens, Ross-Macdonald model, transmission heterogeneity, mixing, vectorial capacity, basic reproduction number, spatial scale, mosquito blood meal, force of infection, epidemic dynamics
MeSH terms
Animals, Communicable Diseases, Disease Outbreaks, Humans, Insect Vectors, Culicidae, Host-Pathogen Interactions

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