August  2015, 20(6): 1685-1713. doi: 10.3934/dcdsb.2015.20.1685

Modeling of contact tracing in epidemic populations structured by disease age

1. 

Department of Mathematics, Vanderbilt University, Nashville, TN 37240, United States

Received  July 2014 Revised  October 2014 Published  June 2015

We consider an age-structured epidemic model with two basic public health interventions: (i) identifying and isolating symptomatic cases, and (ii) tracing and quarantine of the contacts of identified infectives. The dynamics of the infected population are modeled by a nonlinear infection-age-dependent partial differential equation, which is coupled with an ordinary differential equation that describes the dynamics of the susceptible population. Theoretical results about global existence and uniqueness of positive solutions are proved. We also present two practical applications of our model: (1) we assess public health guidelines about emergency preparedness and response in the event of a smallpox bioterrorist attack; (2) we simulate the 2003 SARS outbreak in Taiwan and estimate the number of cases avoided by contact tracing. Our model can be applied as a rational basis for decision makers to guide interventions and deploy public health resources in future epidemics.
Citation: Xi Huo. Modeling of contact tracing in epidemic populations structured by disease age. Discrete & Continuous Dynamical Systems - B, 2015, 20 (6) : 1685-1713. doi: 10.3934/dcdsb.2015.20.1685
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show all references

References:
[1]

Math. Biosci., 195 (2005), 1-22. doi: 10.1016/j.mbs.2005.01.006.  Google Scholar

[2]

J. R. Soc. Interface, 3 (2006), 453-457. doi: 10.1098/rsif.2006.0112.  Google Scholar

[3]

Epidemiology, 16 (2005), 791-801. doi: 10.1097/01.ede.0000181633.80269.4c.  Google Scholar

[4]

Am. J. Epidemiol., 167 (2008), 775-785. doi: 10.1093/aje/kwm375.  Google Scholar

[5]

Morb Mortal Wkly Rep., 290 (2003), 1021-1022. Google Scholar

[6]

Emerg. Infect. Dis., 10 (2004), 825-831. doi: 10.3201/eid1005.030682.  Google Scholar

[7]

Am. J. Epidemiol., 163 (2006), 479-485. doi: 10.1093/aje/kwj056.  Google Scholar

[8]

Am. J. Epidemiol., 158 (2003), 118-128. doi: 10.1093/aje/kwg104.  Google Scholar

[9]

AAPS J., 13 (2011), 427-437. doi: 10.1208/s12248-011-9284-7.  Google Scholar

[10]

Bull. Math. Biol., 69 (2007), 1511-1536. doi: 10.1007/s11538-006-9174-9.  Google Scholar

[11]

J. Theor. Biol., 259 (2009), 165-171. doi: 10.1016/j.jtbi.2009.03.006.  Google Scholar

[12]

Proc. Natl. Acad. Sci. U.S.A., 101 (2004), 6146-6151. doi: 10.1073/pnas.0307506101.  Google Scholar

[13]

Epidemics., 3 (2011), 32-37. doi: 10.1016/j.epidem.2011.01.001.  Google Scholar

[14]

Proc. Biol. Sci., 271 (2004), 2223-2232. doi: 10.1098/rspb.2004.2800.  Google Scholar

[15]

Science., 298 (2002), 1428-1432. doi: 10.1126/science.1074674.  Google Scholar

[16]

Math. Biosci., 180 (2002), 141-160. doi: 10.1016/S0025-5564(02)00111-6.  Google Scholar

[17]

Emerg. Infect. Dis., 10 (2004), 201-206. doi: 10.3201/eid1002.030515.  Google Scholar

[18]

Emerg. Infect. Dis., 9 (2003), 713-717. doi: 10.3201/eid0906.030264.  Google Scholar

[19]

SIAM J. Appl. Math., 66 (2006), 627-647. doi: 10.1137/040615547.  Google Scholar

[20]

Math. Biosci., 216 (2008), 77-89. doi: 10.1016/j.mbs.2008.08.005.  Google Scholar

[21]

Proc. Natl. Acad. Sci. U.S.A., 99 (2002), 10935-10940. doi: 10.1073/pnas.162282799.  Google Scholar

[22]

Math. Biosci., 185 (2003), 33-72. doi: 10.1016/S0025-5564(03)00090-7.  Google Scholar

[23]

Emerg. Infect. Dis., 10 (2004), 832-841. doi: 10.3201/eid1005.030419.  Google Scholar

[24]

Academic Press, 1969. Google Scholar

[25]

Emerg. Infect. Dis., 10 (2004), 207-209. doi: 10.3201/eid1002.030426.  Google Scholar

[26]

Emerg. Infect. Dis., 7 (2001), 959-969. Google Scholar

[27]

Math. Biosci., 164 (2000), 39-64. doi: 10.1016/S0025-5564(99)00061-9.  Google Scholar

[28]

J. Epidemiol. Community Health, 58 (2004), 186-191. doi: 10.1136/jech.2003.014894.  Google Scholar

[29]

Lancet, 361 (2003), 1767-1772. doi: 10.1016/S0140-6736(03)13412-5.  Google Scholar

[30]

E. Rash, Smallpox Overview,, 1977., ().   Google Scholar

[31]

Math. Biosci., 195 (2005), 228-251. doi: 10.1016/j.mbs.2005.03.006.  Google Scholar

[32]

BMC Infect. Dis., 12 (2012), p51. doi: 10.1186/1471-2334-12-51.  Google Scholar

[33]

J. Theor. Biol., 227 (2004), 369-379. doi: 10.1016/j.jtbi.2003.11.014.  Google Scholar

[34]

Monographs and Textbooks in Pure and Applied Mathematics, 89, Marcel Dekker, Inc., New York, 1985.  Google Scholar

[35]

Math. Model. Nat. Phenom., 5 (2010), 191-205. doi: 10.1051/mmnp/20105312.  Google Scholar

[36]

MMWR. Recomm. Rep., 52 (2003), 1-16. Google Scholar

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