On the role of asymptomatic infection in transmission dynamics of infectious diseases.
We propose a compartmental disease transmission model with an asymptomatic (or subclinical) infective class to study the role of asymptomatic infection in the transmission dynamics of infectious diseases with asymptomatic infectives, e.g., influenza. Analytical results are obtained using the respective ratios of susceptible, exposed (incubating), and asymptomatic classes to the clinical symptomatic infective class. Conditions are given for bistability of equilibria to occur, where trajectories with distinct initial values could result in either a major outbreak where the disease spreads to the whole population or a lesser outbreak where some members of the population remain uninfected. This dynamic behavior did not arise in a SARS model without asymptomatic infective class studied by Hsu and Hsieh (SIAM J. Appl. Math. 66(2), 627-647, 2006). Hence, this illustrates that depending on the initial states, control of a disease outbreak with asymptomatic infections may involve more than simply reducing the reproduction number. Moreover, the presence of asymptomatic infections could result in either a positive or negative impact on the outbreak, depending on different sets of conditions on the parameters, as illustrated with numerical simulations. Biological interpretations of the analytical and numerical results are also given.
Hsu
Sze-Bi
SB
Department of Mathematics, National Tsing-Hua University, Hsinchu, Taiwan.
Hsieh
Ying-Hen
YH
D003198:Computer Simulation; D004196:Disease Outbreaks; D006801:Humans; D053124:Influenza A Virus, H5N1 Subtype / Q000254:growth & development*; D007251:Influenza, Human / Q000635:transmission* / Q000821:virology; D008954:Models, Biological
Bull World Health Organ. 1970;42(3):423-7
5310209
JAMA. 1979 Mar 9;241(10):1003-7
368354
Am J Epidemiol. 2004 Apr 1;159(7):623-33
15033640
J Infect Dis. 1998 Apr;177(4):863-73
9534957
Br Med J. 1970 Sep 19;3(5724):676-8
4919024
J Clin Epidemiol. 2003 Dec;56(12):1218-23
14680673
Nature. 2006 Jul 27;442(7101):448-52
16642006
Nature. 2005 Sep 8;437(7056):209-14
16079797
Lancet. 2004 Jan 17;363(9404):234-6
14738798
BMJ. 2005 Nov 12;331(7525):1145
16282424
Bull Math Biol. 2007 May;69(4):1355-75
17318677
Emerg Infect Dis. 2006 Jan;12(1):81-7
16494722
Science. 2005 Aug 12;309(5737):1083-7
16079251
J R Soc Interface. 2006 Jun 22;3(8):453-7
16849273
Proc Natl Acad Sci U S A. 2006 Apr 11;103(15):5935-40
16585506
J Infect Dis. 1980 Sep;142(3):377-83
7003032
Antiviral Res. 1981 Sep;1(3):149-55
7337431
Clin Infect Dis. 2002 May 1;34 Suppl 2:S58-64
11938498