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The Mathematics of Infectious Diseases
Abstract
Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number [Formula: see text], the contact number [Formula: see text], and the replacement number [Formula: see text] are reviewed for the classic SIR epidemic and endemic models. Similar results with new expressions for [Formula: see text] are obtained for MSEIR and SEIR endemic models with either continuous age or age groups. Values of [Formula: see text] and [Formula: see text] are estimated for various diseases including measles in Niger and pertussis in the United States. Previous models with age structure, heterogeneity, and spatial structure are surveyed.
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Cites
Paralytic poliomyelitis: Seasoned strategies, disappearing disease
Hull, H. F., Ward, N. A., Hull, B. P., Milstien, J. B., Hull, H. F., & de Quadros, C. (1994) · The Lancet · doi:10.1016/s0140-6736(94)92472-4 · Cited by 235
Cited by
The Structure and Function of Complex Networks
Newman, M. E. J. (2003) · SIAM Review · doi:10.1137/s003614450342480 · Cited by 18,719
Complex networks: structure and dynamics
BOCCALETTI, S., LATORA, V, MORENO, Y., CHAVEZ, M., & HWANG, D. (2006) · Physics Reports · doi:10.1016/j.physrep.2005.10.009 · Cited by 11,010
Epidemic processes in complex networks
Pastor-Satorras, R., Castellano, C., Van Mieghem, P., & Vespignani, A. (2015) · Reviews of Modern Physics · doi:10.1103/revmodphys.87.925 · Cited by 3,697
The structure and dynamics of multilayer networks
Boccaletti, S., Bianconi, G., Criado, R., del Genio, C. I., Gómez-Gardeñes, J., Romance, M., Sendiña-Nadal, I., Wang, Z., & Zanin, M. (2014) · Physics Reports · doi:10.1016/j.physrep.2014.07.001 · Cited by 3,125
Holme, P., & Saramäki, J. (2012) · Physics Reports · doi:10.1016/j.physrep.2012.03.001 · Cited by 2,736
“belongs to one class or compartment [148,149].”
The BUGS project: evolution, critique and future directions
Lunn, D., Spiegelhalter, D., Thomas, A., & Best, N. (2009) · Statistics in Medicine · doi:10.1002/sim.3680 · Cited by 1,876
Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy
Giordano, G., Blanchini, F., Bruno, R., Colaneri, P., Di Filippo, A., Di Matteo, A., & Colaneri, M. (2020) · Nature Medicine · doi:10.1038/s41591-020-0883-7 · Cited by 1,740
Chains of affection: the structure of adolescent romantic and sexual networks
Bearman, P. S., Moody, J., & Stovel, K. (2004) · American Journal of Sociology · doi:10.1086/386272 · Cited by 817
Modern temporal network theory: a colloquium
Holme, P. (2015) · The European Physical Journal B · doi:10.1140/epjb/e2015-60657-4 · Cited by 734
Network theory and SARS: predicting outbreak diversity
Meyers, L. A., Pourbohloul, B., Newman, M. E. J., Skowronski, D. M., & Brunham, R. C. (2005) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.07.026 · Cited by 705
The benefits and costs of using social distancing to flatten the curve for COVID-19
Thunström, L., Newbold, S. C., Finnoff, D., Ashworth, M., & Shogren, J. F. (2020) · Journal of Benefit-Cost Analysis · doi:10.1017/bca.2020.12 · Cited by 439
Representation learning for dynamic graphs: A survey
Kazemi, S. M., Goel, R., Jain, K., Kobyzev, I., Sethi, A., Forsyth, P., & Poupart, P. (2019) · arXiv · doi:10.48550/arxiv.1905.11485 · Cited by 338
D'Arienzo, M., & Coniglio, A. (2020) · Biosafety and Health · doi:10.1016/j.bsheal.2020.03.004 · Cited by 251
On a temporal model for the Chikungunya disease: Modeling, theory and numerics
Dumont, Y., Chiroleu, F., & Domerg, C. (2008) · Mathematical Biosciences · doi:10.1016/j.mbs.2008.02.008 · Cited by 203
The estimation of the effective reproductive number from disease outbreak data
(2009) · Mathematical Biosciences and Engineering · doi:10.3934/mbe.2009.6.261 · Cited by 128
A critical review of mathematical models and data used in diabetology
Boutayeb, A., & Chetouani, A. (2006) · BioMedical Engineering OnLine · doi:10.1186/1475-925x-5-43 · Cited by 126
What is the best control strategy for multiple infectious disease outbreaks?
Handel, A., Longini, I. M., & Antia, R. (2007) · Proceedings of the Royal Society B: Biological Sciences · doi:10.1098/rspb.2006.0015 · Cited by 94
STSIR: An individual-group game-based model for disclosing virus spread in Social Internet of Things
Wu, G., Xie, L., Zhang, H., Wang, J., Shen, S., & Yu, S. (2023) · Journal of Network and Computer Applications · doi:10.1016/j.jnca.2023.103608 · Cited by 72
Antràs, P., Redding, S., & Rossi-Hansberg, E. (2020) · doi:10.3386/w27840 · Cited by 69
López, M., Peinado, A., & Ortiz, A. (2019) · Computer Networks · doi:10.1016/j.comnet.2019.106945 · Cited by 61
How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks
Grundel, S., Heyder, S., Hotz, T., Ritschel, T. K. S., Sauerteig, P., & Worthmann, K. (2020) · doi:10.1101/2020.12.22.20248707 · Cited by 40
“One of the most popular methodologies for modeling the spread of a virus are so-called compartmental models consisting of difference or differential equations [9].”
MethodWang, Z., Carrasco-Teja, M., Zhang, X., Teichert, G. H., & Garikipati, K. (2021) · Archives of Computational Methods in Engineering · doi:10.1007/s11831-021-09643-1 · Cited by 9
Metadata
- Authors
- Hethcote, H. W.
- Venue
- SIAM Review
- Published
- 2000-01-01
- Volume
- 42
- Issue
- 4
- Pages
- 599-653
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2161728228
- Cited by
- 6,687
- References
- 1
- FWCI
- 24.77
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
