### Abstract

This chapter compiles some of the results on influenza dynamics that involve a single strain, as well as two competing strains. The emphasis is on the role of cross-immunity, quarantine and age-structure as mechanisms capable of supporting recurrent influenza epidemic outbreaks. Quarantine or age-structure alone can support oscillations while cross-immunity enhances the likelihood of strain coexistence and impacts the length of the period. It is the hope that the perspective provided here will instigate others to use mathematical models in the study of disease transmission and its evolution, particularly in a setting that involves highly variable pathogens.

Original language | English (US) |
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Title of host publication | Lecture Notes in Mathematics |

Pages | 349-364 |

Number of pages | 16 |

Volume | 1945 |

DOIs | |

State | Published - 2008 |

### Publication series

Name | Lecture Notes in Mathematics |
---|---|

Volume | 1945 |

ISSN (Print) | 00758434 |

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### ASJC Scopus subject areas

- Mathematics (miscellaneous)

### Cite this

*Lecture Notes in Mathematics*(Vol. 1945, pp. 349-364). (Lecture Notes in Mathematics; Vol. 1945). https://doi.org/10.1007/978-3-540-78911-6_13

**Mathematical models of influenza : The role of cross-immunity, quarantine and age-structure.** / Nuño, M.; Castillo-Chavez, Carlos; Feng, Z.; Martcheva, M.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Lecture Notes in Mathematics.*vol. 1945, Lecture Notes in Mathematics, vol. 1945, pp. 349-364. https://doi.org/10.1007/978-3-540-78911-6_13

}

TY - CHAP

T1 - Mathematical models of influenza

T2 - The role of cross-immunity, quarantine and age-structure

AU - Nuño, M.

AU - Castillo-Chavez, Carlos

AU - Feng, Z.

AU - Martcheva, M.

PY - 2008

Y1 - 2008

N2 - This chapter compiles some of the results on influenza dynamics that involve a single strain, as well as two competing strains. The emphasis is on the role of cross-immunity, quarantine and age-structure as mechanisms capable of supporting recurrent influenza epidemic outbreaks. Quarantine or age-structure alone can support oscillations while cross-immunity enhances the likelihood of strain coexistence and impacts the length of the period. It is the hope that the perspective provided here will instigate others to use mathematical models in the study of disease transmission and its evolution, particularly in a setting that involves highly variable pathogens.

AB - This chapter compiles some of the results on influenza dynamics that involve a single strain, as well as two competing strains. The emphasis is on the role of cross-immunity, quarantine and age-structure as mechanisms capable of supporting recurrent influenza epidemic outbreaks. Quarantine or age-structure alone can support oscillations while cross-immunity enhances the likelihood of strain coexistence and impacts the length of the period. It is the hope that the perspective provided here will instigate others to use mathematical models in the study of disease transmission and its evolution, particularly in a setting that involves highly variable pathogens.

UR - http://www.scopus.com/inward/record.url?scp=42249083000&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=42249083000&partnerID=8YFLogxK

U2 - 10.1007/978-3-540-78911-6_13

DO - 10.1007/978-3-540-78911-6_13

M3 - Chapter

SN - 9783540789109

VL - 1945

T3 - Lecture Notes in Mathematics

SP - 349

EP - 364

BT - Lecture Notes in Mathematics

ER -