Global analysis for spread of infectious diseases via transportation networks View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

2015-05

AUTHORS

Yukihiko Nakata, Gergely Röst

ABSTRACT

We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay differential equations. We define the basic reproduction number R(0) as the spectral radius of a next generation matrix. For multi-regional systems with strongly connected transportation networks, we prove that if R(0) ≤ 1 then the disease will be eradicated from each region, while if R(0) > 1 there is a globally asymptotically stable equilibrium, which is endemic in every region. If the transportation network is not strongly connected, then the model analysis shows that numerous endemic patterns can exist by admitting a globally asymptotically stable equilibrium, which may be disease free in some regions while endemic in other regions. We provide a procedure to detect the disease free and the endemic regions according to the network topology and local reproduction numbers. The main ingredients of the mathematical proofs are the inductive applications of the theory of asymptotically autonomous semiflows and cooperative dynamical systems. We visualise stability boundaries of equilibria in a parameter plane to illustrate the influence of the transportation network on the disease dynamics. For a system consisting of two regions, we find that due to spatial heterogeneity characterised by different local reproduction numbers, R(0) may depend non-monotonically on the dispersal rates, thus travel restrictions are not always beneficial. More... »

PAGES

1411-1456

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s00285-014-0801-z

DOI

http://dx.doi.org/10.1007/s00285-014-0801-z

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1053123989

PUBMED

https://www.ncbi.nlm.nih.gov/pubmed/24948128


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Basic Reproduction Number", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Communicable Diseases", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Epidemics", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Global Health", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Humans", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Mathematical Concepts", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Models, Biological", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Population Dynamics", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Transportation", 
        "type": "DefinedTerm"
      }, 
      {
        "inDefinedTermSet": "https://www.nlm.nih.gov/mesh/", 
        "name": "Travel", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "University of Tokyo", 
          "id": "https://www.grid.ac/institutes/grid.26999.3d", 
          "name": [
            "Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1., 6720, Szeged, Hungary", 
            "Graduate School of Mathematical Sciences, University of Tokyo, Meguroku Komaba 3-8-1, Tokyo, Japan"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Nakata", 
        "givenName": "Yukihiko", 
        "id": "sg:person.01344110455.31", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01344110455.31"
        ], 
        "type": "Person"
      }, 
      {
        "affiliation": {
          "alternateName": "University of Szeged", 
          "id": "https://www.grid.ac/institutes/grid.9008.1", 
          "name": [
            "Bolyai Institute, University of Szeged, Aradi v\u00e9rtan\u00fak tere 1., 6720, Szeged, Hungary", 
            "MTA-SZTE Analysis and Stochastics Research Group, Szeged, Hungary"
          ], 
          "type": "Organization"
        }, 
        "familyName": "R\u00f6st", 
        "givenName": "Gergely", 
        "id": "sg:person.0733700407.59", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0733700407.59"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "https://doi.org/10.1080/08898480306720", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1001014121"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1371/journal.pone.0009548", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1005219569"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/srep00476", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006559387", 
          "https://doi.org/10.1038/srep00476"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jtbi.2008.05.026", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1006732661"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-7646-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007500442", 
          "https://doi.org/10.1007/978-1-4419-7646-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4419-7646-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1007500442", 
          "https://doi.org/10.1007/978-1-4419-7646-8"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/srep00062", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1008122163", 
          "https://doi.org/10.1038/srep00062"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mbs.2002.11.001", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1010184102"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1090/s0002-9939-00-05564-7", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011583717"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.mbs.2005.09.002", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1011797270"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jtbi.2005.08.005", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1014598482"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1371/journal.pone.0019869", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1017412360"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s11538-006-9169-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1018294991", 
          "https://doi.org/10.1007/s11538-006-9169-6"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1098/rsif.2006.0112", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019237390"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jtbi.2006.03.018", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1019795376"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1371/journal.pone.0000401", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1021802869"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.na.2011.07.024", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1023922450"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jtbi.2007.11.028", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024369081"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1073/pnas.0510525103", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1024622397"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0140-6736(09)60209-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1025648052"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0025-5564(02)00108-6", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1029513709"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1371/journal.pone.0016591", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031090198"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1056/nejmoa031349", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1031479246"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.3201/eid1011.040729", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1032542599"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://app.dimensions.ai/details/publication/pub.1033091385", 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-4206-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033091385", 
          "https://doi.org/10.1007/978-1-4612-4206-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-1-4612-4206-2", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033091385", 
          "https://doi.org/10.1007/978-1-4612-4206-2"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00285-009-0280-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033370447", 
          "https://doi.org/10.1007/s00285-009-0280-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00285-009-0280-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033370447", 
          "https://doi.org/10.1007/s00285-009-0280-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/s00285-009-0280-9", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1033370447", 
          "https://doi.org/10.1007/s00285-009-0280-9"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.nonrwa.2011.05.004", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035030948"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1056/nejmc0904559", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1035997600"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1093/imammb/dqi003", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1036872921"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0140-6736(05)71089-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1038834743"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00178324", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039188921", 
          "https://doi.org/10.1007/bf00178324"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.99.148701", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039549524"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1103/physrevlett.99.148701", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1039549524"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-3-540-34426-1_4", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040486618", 
          "https://doi.org/10.1007/978-3-540-34426-1_4"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s1473-3099(10)70223-1", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047079625"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00173267", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047159252", 
          "https://doi.org/10.1007/bf00173267"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/bf00173267", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1047159252", 
          "https://doi.org/10.1007/bf00173267"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/j.jmaa.2006.07.057", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049813183"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/nphys1944", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1049840682", 
          "https://doi.org/10.1038/nphys1944"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1016/s0025-5564(01)00057-8", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1050994641"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/nm0506-497", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051165005", 
          "https://doi.org/10.1038/nm0506-497"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1038/nm0506-497", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1051165005", 
          "https://doi.org/10.1038/nm0506-497"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/110850761", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062865423"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/130914127", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062870596"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/s0036139903431245", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1062874949"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1216/rmj-2008-38-5-1525", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1064428643"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1142/9789812798893_0020", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1088782005"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1137/1.9781611971262", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098553024"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "https://doi.org/10.1017/cbo9780511530043", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1098705552"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-009-4335-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109716601", 
          "https://doi.org/10.1007/978-94-009-4335-3"
        ], 
        "type": "CreativeWork"
      }, 
      {
        "id": "sg:pub.10.1007/978-94-009-4335-3", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1109716601", 
          "https://doi.org/10.1007/978-94-009-4335-3"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "2015-05", 
    "datePublishedReg": "2015-05-01", 
    "description": "We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay differential equations. We define the basic reproduction number R(0) as the spectral radius of a next generation matrix. For multi-regional systems with strongly connected transportation networks, we prove that if R(0) \u2264 1 then the disease will be eradicated from each region, while if R(0) > 1 there is a globally asymptotically stable equilibrium, which is endemic in every region. If the transportation network is not strongly connected, then the model analysis shows that numerous endemic patterns can exist by admitting a globally asymptotically stable equilibrium, which may be disease free in some regions while endemic in other regions. We provide a procedure to detect the disease free and the endemic regions according to the network topology and local reproduction numbers. The main ingredients of the mathematical proofs are the inductive applications of the theory of asymptotically autonomous semiflows and cooperative dynamical systems. We visualise stability boundaries of equilibria in a parameter plane to illustrate the influence of the transportation network on the disease dynamics. For a system consisting of two regions, we find that due to spatial heterogeneity characterised by different local reproduction numbers, R(0) may depend non-monotonically on the dispersal rates, thus travel restrictions are not always beneficial.", 
    "genre": "research_article", 
    "id": "sg:pub.10.1007/s00285-014-0801-z", 
    "inLanguage": [
      "en"
    ], 
    "isAccessibleForFree": true, 
    "isFundedItemOf": [
      {
        "id": "sg:grant.5994718", 
        "type": "MonetaryGrant"
      }, 
      {
        "id": "sg:grant.4187940", 
        "type": "MonetaryGrant"
      }, 
      {
        "id": "sg:grant.3783763", 
        "type": "MonetaryGrant"
      }, 
      {
        "id": "sg:grant.3781549", 
        "type": "MonetaryGrant"
      }, 
      {
        "id": "sg:grant.5992837", 
        "type": "MonetaryGrant"
      }
    ], 
    "isPartOf": [
      {
        "id": "sg:journal.1081642", 
        "issn": [
          "0303-6812", 
          "1432-1416"
        ], 
        "name": "Journal of Mathematical Biology", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "6", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "70"
      }
    ], 
    "name": "Global analysis for spread of infectious diseases via transportation networks", 
    "pagination": "1411-1456", 
    "productId": [
      {
        "name": "readcube_id", 
        "type": "PropertyValue", 
        "value": [
          "fd0ac25c99a5e5505818afe7923a100d0911601fd7a6f323eb06ce27c71fc837"
        ]
      }, 
      {
        "name": "pubmed_id", 
        "type": "PropertyValue", 
        "value": [
          "24948128"
        ]
      }, 
      {
        "name": "nlm_unique_id", 
        "type": "PropertyValue", 
        "value": [
          "7502105"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/s00285-014-0801-z"
        ]
      }, 
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1053123989"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/s00285-014-0801-z", 
      "https://app.dimensions.ai/details/publication/pub.1053123989"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2019-04-11T00:29", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-uberresearch-data-dimensions-target-20181106-alternative/cleanup/v134/2549eaecd7973599484d7c17b260dba0a4ecb94b/merge/v9/a6c9fde33151104705d4d7ff012ea9563521a3ce/jats-lookup/v90/0000000001_0000000264/records_8695_00000596.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "http://link.springer.com/10.1007%2Fs00285-014-0801-z"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/s00285-014-0801-z'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/s00285-014-0801-z'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/s00285-014-0801-z'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/s00285-014-0801-z'


 

This table displays all metadata directly associated to this object as RDF triples.

283 TRIPLES      21 PREDICATES      86 URIs      31 LITERALS      19 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/s00285-014-0801-z schema:about N0866170e8e2141139798393fc0087d95
2 N2e89e6e21f9746249eee393543097bd7
3 N5e7af42ac490467590888aee9d81a623
4 N61f9dfb339a646218608d9330a4cb67c
5 N6bdb032d5a624285a04ee7e666ceb091
6 Nb1da36016c644b3e921fc181c51493c2
7 Nb5b485983655419babcd6b789f93a56f
8 Nb6a20fbcfeef4f56b8b5b47021b73017
9 Ne4d1910d776f41af9920d09cd931ec1a
10 Nf7930efd5a08435c916889aeddaf6a1f
11 anzsrc-for:01
12 anzsrc-for:0102
13 schema:author Nadd42a36a451464faa662e49260d09a5
14 schema:citation sg:pub.10.1007/978-1-4419-7646-8
15 sg:pub.10.1007/978-1-4612-4206-2
16 sg:pub.10.1007/978-3-540-34426-1_4
17 sg:pub.10.1007/978-94-009-4335-3
18 sg:pub.10.1007/bf00173267
19 sg:pub.10.1007/bf00178324
20 sg:pub.10.1007/s00285-009-0280-9
21 sg:pub.10.1007/s11538-006-9169-6
22 sg:pub.10.1038/nm0506-497
23 sg:pub.10.1038/nphys1944
24 sg:pub.10.1038/srep00062
25 sg:pub.10.1038/srep00476
26 https://app.dimensions.ai/details/publication/pub.1033091385
27 https://doi.org/10.1016/j.jmaa.2006.07.057
28 https://doi.org/10.1016/j.jtbi.2005.08.005
29 https://doi.org/10.1016/j.jtbi.2006.03.018
30 https://doi.org/10.1016/j.jtbi.2007.11.028
31 https://doi.org/10.1016/j.jtbi.2008.05.026
32 https://doi.org/10.1016/j.mbs.2002.11.001
33 https://doi.org/10.1016/j.mbs.2005.09.002
34 https://doi.org/10.1016/j.na.2011.07.024
35 https://doi.org/10.1016/j.nonrwa.2011.05.004
36 https://doi.org/10.1016/s0025-5564(01)00057-8
37 https://doi.org/10.1016/s0025-5564(02)00108-6
38 https://doi.org/10.1016/s0140-6736(05)71089-8
39 https://doi.org/10.1016/s0140-6736(09)60209-9
40 https://doi.org/10.1016/s1473-3099(10)70223-1
41 https://doi.org/10.1017/cbo9780511530043
42 https://doi.org/10.1056/nejmc0904559
43 https://doi.org/10.1056/nejmoa031349
44 https://doi.org/10.1073/pnas.0510525103
45 https://doi.org/10.1080/08898480306720
46 https://doi.org/10.1090/s0002-9939-00-05564-7
47 https://doi.org/10.1093/imammb/dqi003
48 https://doi.org/10.1098/rsif.2006.0112
49 https://doi.org/10.1103/physrevlett.99.148701
50 https://doi.org/10.1137/1.9781611971262
51 https://doi.org/10.1137/110850761
52 https://doi.org/10.1137/130914127
53 https://doi.org/10.1137/s0036139903431245
54 https://doi.org/10.1142/9789812798893_0020
55 https://doi.org/10.1216/rmj-2008-38-5-1525
56 https://doi.org/10.1371/journal.pone.0000401
57 https://doi.org/10.1371/journal.pone.0009548
58 https://doi.org/10.1371/journal.pone.0016591
59 https://doi.org/10.1371/journal.pone.0019869
60 https://doi.org/10.3201/eid1011.040729
61 schema:datePublished 2015-05
62 schema:datePublishedReg 2015-05-01
63 schema:description We formulate an epidemic model for the spread of an infectious disease along with population dispersal over an arbitrary number of distinct regions. Structuring the population by the time elapsed since the start of travel, we describe the infectious disease dynamics during transportation as well as in the regions. As a result, we obtain a system of delay differential equations. We define the basic reproduction number R(0) as the spectral radius of a next generation matrix. For multi-regional systems with strongly connected transportation networks, we prove that if R(0) ≤ 1 then the disease will be eradicated from each region, while if R(0) > 1 there is a globally asymptotically stable equilibrium, which is endemic in every region. If the transportation network is not strongly connected, then the model analysis shows that numerous endemic patterns can exist by admitting a globally asymptotically stable equilibrium, which may be disease free in some regions while endemic in other regions. We provide a procedure to detect the disease free and the endemic regions according to the network topology and local reproduction numbers. The main ingredients of the mathematical proofs are the inductive applications of the theory of asymptotically autonomous semiflows and cooperative dynamical systems. We visualise stability boundaries of equilibria in a parameter plane to illustrate the influence of the transportation network on the disease dynamics. For a system consisting of two regions, we find that due to spatial heterogeneity characterised by different local reproduction numbers, R(0) may depend non-monotonically on the dispersal rates, thus travel restrictions are not always beneficial.
64 schema:genre research_article
65 schema:inLanguage en
66 schema:isAccessibleForFree true
67 schema:isPartOf N588b2c65c4e04be5a57502e12090a9c2
68 N9439e0ded35440cba70cb9c7709ca627
69 sg:journal.1081642
70 schema:name Global analysis for spread of infectious diseases via transportation networks
71 schema:pagination 1411-1456
72 schema:productId N69df58a7b0e147abbdfa044da102f002
73 Nc10a62be46094b93bc67fce5304ba3f9
74 Nc28c958b44a54a0d949869a76339a0c5
75 Nc2f343a0fa1f436dbabc882a101c23b1
76 Neba7969a9c954910a859f2a8fc4f3a21
77 schema:sameAs https://app.dimensions.ai/details/publication/pub.1053123989
78 https://doi.org/10.1007/s00285-014-0801-z
79 schema:sdDatePublished 2019-04-11T00:29
80 schema:sdLicense https://scigraph.springernature.com/explorer/license/
81 schema:sdPublisher Ne9e228146a97455aa3a927dded5fa110
82 schema:url http://link.springer.com/10.1007%2Fs00285-014-0801-z
83 sgo:license sg:explorer/license/
84 sgo:sdDataset articles
85 rdf:type schema:ScholarlyArticle
86 N0866170e8e2141139798393fc0087d95 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
87 schema:name Basic Reproduction Number
88 rdf:type schema:DefinedTerm
89 N2e89e6e21f9746249eee393543097bd7 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
90 schema:name Models, Biological
91 rdf:type schema:DefinedTerm
92 N588b2c65c4e04be5a57502e12090a9c2 schema:issueNumber 6
93 rdf:type schema:PublicationIssue
94 N5e7af42ac490467590888aee9d81a623 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
95 schema:name Transportation
96 rdf:type schema:DefinedTerm
97 N61f9dfb339a646218608d9330a4cb67c schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
98 schema:name Population Dynamics
99 rdf:type schema:DefinedTerm
100 N69df58a7b0e147abbdfa044da102f002 schema:name pubmed_id
101 schema:value 24948128
102 rdf:type schema:PropertyValue
103 N6bdb032d5a624285a04ee7e666ceb091 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
104 schema:name Epidemics
105 rdf:type schema:DefinedTerm
106 N738f7b46ec284540ad4f29d7736315eb rdf:first sg:person.0733700407.59
107 rdf:rest rdf:nil
108 N9439e0ded35440cba70cb9c7709ca627 schema:volumeNumber 70
109 rdf:type schema:PublicationVolume
110 Nadd42a36a451464faa662e49260d09a5 rdf:first sg:person.01344110455.31
111 rdf:rest N738f7b46ec284540ad4f29d7736315eb
112 Nb1da36016c644b3e921fc181c51493c2 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
113 schema:name Travel
114 rdf:type schema:DefinedTerm
115 Nb5b485983655419babcd6b789f93a56f schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
116 schema:name Mathematical Concepts
117 rdf:type schema:DefinedTerm
118 Nb6a20fbcfeef4f56b8b5b47021b73017 schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
119 schema:name Humans
120 rdf:type schema:DefinedTerm
121 Nc10a62be46094b93bc67fce5304ba3f9 schema:name dimensions_id
122 schema:value pub.1053123989
123 rdf:type schema:PropertyValue
124 Nc28c958b44a54a0d949869a76339a0c5 schema:name doi
125 schema:value 10.1007/s00285-014-0801-z
126 rdf:type schema:PropertyValue
127 Nc2f343a0fa1f436dbabc882a101c23b1 schema:name readcube_id
128 schema:value fd0ac25c99a5e5505818afe7923a100d0911601fd7a6f323eb06ce27c71fc837
129 rdf:type schema:PropertyValue
130 Ne4d1910d776f41af9920d09cd931ec1a schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
131 schema:name Global Health
132 rdf:type schema:DefinedTerm
133 Ne9e228146a97455aa3a927dded5fa110 schema:name Springer Nature - SN SciGraph project
134 rdf:type schema:Organization
135 Neba7969a9c954910a859f2a8fc4f3a21 schema:name nlm_unique_id
136 schema:value 7502105
137 rdf:type schema:PropertyValue
138 Nf7930efd5a08435c916889aeddaf6a1f schema:inDefinedTermSet https://www.nlm.nih.gov/mesh/
139 schema:name Communicable Diseases
140 rdf:type schema:DefinedTerm
141 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
142 schema:name Mathematical Sciences
143 rdf:type schema:DefinedTerm
144 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
145 schema:name Applied Mathematics
146 rdf:type schema:DefinedTerm
147 sg:grant.3781549 http://pending.schema.org/fundedItem sg:pub.10.1007/s00285-014-0801-z
148 rdf:type schema:MonetaryGrant
149 sg:grant.3783763 http://pending.schema.org/fundedItem sg:pub.10.1007/s00285-014-0801-z
150 rdf:type schema:MonetaryGrant
151 sg:grant.4187940 http://pending.schema.org/fundedItem sg:pub.10.1007/s00285-014-0801-z
152 rdf:type schema:MonetaryGrant
153 sg:grant.5992837 http://pending.schema.org/fundedItem sg:pub.10.1007/s00285-014-0801-z
154 rdf:type schema:MonetaryGrant
155 sg:grant.5994718 http://pending.schema.org/fundedItem sg:pub.10.1007/s00285-014-0801-z
156 rdf:type schema:MonetaryGrant
157 sg:journal.1081642 schema:issn 0303-6812
158 1432-1416
159 schema:name Journal of Mathematical Biology
160 rdf:type schema:Periodical
161 sg:person.01344110455.31 schema:affiliation https://www.grid.ac/institutes/grid.26999.3d
162 schema:familyName Nakata
163 schema:givenName Yukihiko
164 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.01344110455.31
165 rdf:type schema:Person
166 sg:person.0733700407.59 schema:affiliation https://www.grid.ac/institutes/grid.9008.1
167 schema:familyName Röst
168 schema:givenName Gergely
169 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.0733700407.59
170 rdf:type schema:Person
171 sg:pub.10.1007/978-1-4419-7646-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1007500442
172 https://doi.org/10.1007/978-1-4419-7646-8
173 rdf:type schema:CreativeWork
174 sg:pub.10.1007/978-1-4612-4206-2 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033091385
175 https://doi.org/10.1007/978-1-4612-4206-2
176 rdf:type schema:CreativeWork
177 sg:pub.10.1007/978-3-540-34426-1_4 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040486618
178 https://doi.org/10.1007/978-3-540-34426-1_4
179 rdf:type schema:CreativeWork
180 sg:pub.10.1007/978-94-009-4335-3 schema:sameAs https://app.dimensions.ai/details/publication/pub.1109716601
181 https://doi.org/10.1007/978-94-009-4335-3
182 rdf:type schema:CreativeWork
183 sg:pub.10.1007/bf00173267 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047159252
184 https://doi.org/10.1007/bf00173267
185 rdf:type schema:CreativeWork
186 sg:pub.10.1007/bf00178324 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039188921
187 https://doi.org/10.1007/bf00178324
188 rdf:type schema:CreativeWork
189 sg:pub.10.1007/s00285-009-0280-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1033370447
190 https://doi.org/10.1007/s00285-009-0280-9
191 rdf:type schema:CreativeWork
192 sg:pub.10.1007/s11538-006-9169-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1018294991
193 https://doi.org/10.1007/s11538-006-9169-6
194 rdf:type schema:CreativeWork
195 sg:pub.10.1038/nm0506-497 schema:sameAs https://app.dimensions.ai/details/publication/pub.1051165005
196 https://doi.org/10.1038/nm0506-497
197 rdf:type schema:CreativeWork
198 sg:pub.10.1038/nphys1944 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049840682
199 https://doi.org/10.1038/nphys1944
200 rdf:type schema:CreativeWork
201 sg:pub.10.1038/srep00062 schema:sameAs https://app.dimensions.ai/details/publication/pub.1008122163
202 https://doi.org/10.1038/srep00062
203 rdf:type schema:CreativeWork
204 sg:pub.10.1038/srep00476 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006559387
205 https://doi.org/10.1038/srep00476
206 rdf:type schema:CreativeWork
207 https://app.dimensions.ai/details/publication/pub.1033091385 schema:CreativeWork
208 https://doi.org/10.1016/j.jmaa.2006.07.057 schema:sameAs https://app.dimensions.ai/details/publication/pub.1049813183
209 rdf:type schema:CreativeWork
210 https://doi.org/10.1016/j.jtbi.2005.08.005 schema:sameAs https://app.dimensions.ai/details/publication/pub.1014598482
211 rdf:type schema:CreativeWork
212 https://doi.org/10.1016/j.jtbi.2006.03.018 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019795376
213 rdf:type schema:CreativeWork
214 https://doi.org/10.1016/j.jtbi.2007.11.028 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024369081
215 rdf:type schema:CreativeWork
216 https://doi.org/10.1016/j.jtbi.2008.05.026 schema:sameAs https://app.dimensions.ai/details/publication/pub.1006732661
217 rdf:type schema:CreativeWork
218 https://doi.org/10.1016/j.mbs.2002.11.001 schema:sameAs https://app.dimensions.ai/details/publication/pub.1010184102
219 rdf:type schema:CreativeWork
220 https://doi.org/10.1016/j.mbs.2005.09.002 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011797270
221 rdf:type schema:CreativeWork
222 https://doi.org/10.1016/j.na.2011.07.024 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023922450
223 rdf:type schema:CreativeWork
224 https://doi.org/10.1016/j.nonrwa.2011.05.004 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035030948
225 rdf:type schema:CreativeWork
226 https://doi.org/10.1016/s0025-5564(01)00057-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1050994641
227 rdf:type schema:CreativeWork
228 https://doi.org/10.1016/s0025-5564(02)00108-6 schema:sameAs https://app.dimensions.ai/details/publication/pub.1029513709
229 rdf:type schema:CreativeWork
230 https://doi.org/10.1016/s0140-6736(05)71089-8 schema:sameAs https://app.dimensions.ai/details/publication/pub.1038834743
231 rdf:type schema:CreativeWork
232 https://doi.org/10.1016/s0140-6736(09)60209-9 schema:sameAs https://app.dimensions.ai/details/publication/pub.1025648052
233 rdf:type schema:CreativeWork
234 https://doi.org/10.1016/s1473-3099(10)70223-1 schema:sameAs https://app.dimensions.ai/details/publication/pub.1047079625
235 rdf:type schema:CreativeWork
236 https://doi.org/10.1017/cbo9780511530043 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098705552
237 rdf:type schema:CreativeWork
238 https://doi.org/10.1056/nejmc0904559 schema:sameAs https://app.dimensions.ai/details/publication/pub.1035997600
239 rdf:type schema:CreativeWork
240 https://doi.org/10.1056/nejmoa031349 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031479246
241 rdf:type schema:CreativeWork
242 https://doi.org/10.1073/pnas.0510525103 schema:sameAs https://app.dimensions.ai/details/publication/pub.1024622397
243 rdf:type schema:CreativeWork
244 https://doi.org/10.1080/08898480306720 schema:sameAs https://app.dimensions.ai/details/publication/pub.1001014121
245 rdf:type schema:CreativeWork
246 https://doi.org/10.1090/s0002-9939-00-05564-7 schema:sameAs https://app.dimensions.ai/details/publication/pub.1011583717
247 rdf:type schema:CreativeWork
248 https://doi.org/10.1093/imammb/dqi003 schema:sameAs https://app.dimensions.ai/details/publication/pub.1036872921
249 rdf:type schema:CreativeWork
250 https://doi.org/10.1098/rsif.2006.0112 schema:sameAs https://app.dimensions.ai/details/publication/pub.1019237390
251 rdf:type schema:CreativeWork
252 https://doi.org/10.1103/physrevlett.99.148701 schema:sameAs https://app.dimensions.ai/details/publication/pub.1039549524
253 rdf:type schema:CreativeWork
254 https://doi.org/10.1137/1.9781611971262 schema:sameAs https://app.dimensions.ai/details/publication/pub.1098553024
255 rdf:type schema:CreativeWork
256 https://doi.org/10.1137/110850761 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062865423
257 rdf:type schema:CreativeWork
258 https://doi.org/10.1137/130914127 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062870596
259 rdf:type schema:CreativeWork
260 https://doi.org/10.1137/s0036139903431245 schema:sameAs https://app.dimensions.ai/details/publication/pub.1062874949
261 rdf:type schema:CreativeWork
262 https://doi.org/10.1142/9789812798893_0020 schema:sameAs https://app.dimensions.ai/details/publication/pub.1088782005
263 rdf:type schema:CreativeWork
264 https://doi.org/10.1216/rmj-2008-38-5-1525 schema:sameAs https://app.dimensions.ai/details/publication/pub.1064428643
265 rdf:type schema:CreativeWork
266 https://doi.org/10.1371/journal.pone.0000401 schema:sameAs https://app.dimensions.ai/details/publication/pub.1021802869
267 rdf:type schema:CreativeWork
268 https://doi.org/10.1371/journal.pone.0009548 schema:sameAs https://app.dimensions.ai/details/publication/pub.1005219569
269 rdf:type schema:CreativeWork
270 https://doi.org/10.1371/journal.pone.0016591 schema:sameAs https://app.dimensions.ai/details/publication/pub.1031090198
271 rdf:type schema:CreativeWork
272 https://doi.org/10.1371/journal.pone.0019869 schema:sameAs https://app.dimensions.ai/details/publication/pub.1017412360
273 rdf:type schema:CreativeWork
274 https://doi.org/10.3201/eid1011.040729 schema:sameAs https://app.dimensions.ai/details/publication/pub.1032542599
275 rdf:type schema:CreativeWork
276 https://www.grid.ac/institutes/grid.26999.3d schema:alternateName University of Tokyo
277 schema:name Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., 6720, Szeged, Hungary
278 Graduate School of Mathematical Sciences, University of Tokyo, Meguroku Komaba 3-8-1, Tokyo, Japan
279 rdf:type schema:Organization
280 https://www.grid.ac/institutes/grid.9008.1 schema:alternateName University of Szeged
281 schema:name Bolyai Institute, University of Szeged, Aradi vértanúk tere 1., 6720, Szeged, Hungary
282 MTA-SZTE Analysis and Stochastics Research Group, Szeged, Hungary
283 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...