Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus

Alexandra Hogan; Katie Glass; Hannah Moore; Robert S Anderssen

doi:10.1007/978-4-431-55342-7_9

Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus

Alexandra Hogan, Katie Glass, Hannah Moore, Robert S Anderssen

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

Mathematical modelling plays an important role in understanding the dynamics of transmissible infections, as information about the drivers of infectious disease outbreaks can help inform health care planning and interventions. This paper provides some background about the mathematics of infectious disease modelling. Using a common childhood infection as a case study, age structures in compartmental differential equation models are explored. The qualitative characteristics of the numerical results for different models are discussed, and the benefits of incorporating age structures in these models are examined. This research demonstrates that, for the SIR-type model considered, the inclusion of age structures does not change the overall qualitative dynamics predicted by that model. Focussing on only a single age class then simplifies model analysis. However, age differentiation remains useful for simulating age-dependent intervention strategies such as vaccination.

Original language	English
Title of host publication	Applications + Practical Conceptualization + Mathematics = fruitful Innovation
Editors	R.S. Anderssen
Place of Publication	Tokyo, Japan
Publisher	Springer Japan KK
Pages	105-116
Edition	Peer reviewed
ISBN (Print)	978443155342
DOIs	https://doi.org/10.1007/978-4-431-55342-7_9
Publication status	Published - 2015
Event	Proceedings of the Forum for Mathematics for Industry 2014 - Fukuoka, Japan Duration: 1 Jan 2015 → … http://www.springer.com/us/book/9784431553410

Conference

Conference	Proceedings of the Forum for Mathematics for Industry 2014
Period	1/01/15 → …
Other	October 27-31 2014
Internet address	http://www.springer.com/us/book/9784431553410

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10.1007/978-4-431-55342-7_9

Cite this

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title = "Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus",

abstract = "Mathematical modelling plays an important role in understanding the dynamics of transmissible infections, as information about the drivers of infectious disease outbreaks can help inform health care planning and interventions. This paper provides some background about the mathematics of infectious disease modelling. Using a common childhood infection as a case study, age structures in compartmental differential equation models are explored. The qualitative characteristics of the numerical results for different models are discussed, and the benefits of incorporating age structures in these models are examined. This research demonstrates that, for the SIR-type model considered, the inclusion of age structures does not change the overall qualitative dynamics predicted by that model. Focussing on only a single age class then simplifies model analysis. However, age differentiation remains useful for simulating age-dependent intervention strategies such as vaccination.",

author = "Alexandra Hogan and Katie Glass and Hannah Moore and Anderssen, {Robert S}",

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editor = "{R.S. Anderssen}",

booktitle = "Applications + Practical Conceptualization + Mathematics = fruitful Innovation",

publisher = "Springer Japan KK",

edition = "Peer reviewed",

note = "Proceedings of the Forum for Mathematics for Industry 2014 ; Conference date: 01-01-2015",

url = "http://www.springer.com/us/book/9784431553410",

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Hogan, A, Glass, K, Moore, H & Anderssen, RS 2015, Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus. in RSA (ed.), Applications + Practical Conceptualization + Mathematics = fruitful Innovation. Peer reviewed edn, Springer Japan KK, Tokyo, Japan, pp. 105-116, Proceedings of the Forum for Mathematics for Industry 2014, 1/01/15. https://doi.org/10.1007/978-4-431-55342-7_9

Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus. / Hogan, Alexandra; Glass, Katie; Moore, Hannah et al.
Applications + Practical Conceptualization + Mathematics = fruitful Innovation. ed. / R.S. Anderssen. Peer reviewed. ed. Tokyo, Japan: Springer Japan KK, 2015. p. 105-116.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AU - Glass, Katie

AU - Moore, Hannah

AU - Anderssen, Robert S

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N2 - Mathematical modelling plays an important role in understanding the dynamics of transmissible infections, as information about the drivers of infectious disease outbreaks can help inform health care planning and interventions. This paper provides some background about the mathematics of infectious disease modelling. Using a common childhood infection as a case study, age structures in compartmental differential equation models are explored. The qualitative characteristics of the numerical results for different models are discussed, and the benefits of incorporating age structures in these models are examined. This research demonstrates that, for the SIR-type model considered, the inclusion of age structures does not change the overall qualitative dynamics predicted by that model. Focussing on only a single age class then simplifies model analysis. However, age differentiation remains useful for simulating age-dependent intervention strategies such as vaccination.

AB - Mathematical modelling plays an important role in understanding the dynamics of transmissible infections, as information about the drivers of infectious disease outbreaks can help inform health care planning and interventions. This paper provides some background about the mathematics of infectious disease modelling. Using a common childhood infection as a case study, age structures in compartmental differential equation models are explored. The qualitative characteristics of the numerical results for different models are discussed, and the benefits of incorporating age structures in these models are examined. This research demonstrates that, for the SIR-type model considered, the inclusion of age structures does not change the overall qualitative dynamics predicted by that model. Focussing on only a single age class then simplifies model analysis. However, age differentiation remains useful for simulating age-dependent intervention strategies such as vaccination.

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BT - Applications + Practical Conceptualization + Mathematics = fruitful Innovation

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T2 - Proceedings of the Forum for Mathematics for Industry 2014

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Age structures in mathematical models for infectious diseases, with a case study of respiratory syncytial virus

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