No one Set of Parameter Values Can Simulate the Epidemics Due to SARS Occurring at Different Localities
A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.
[1] Communicable Disease Surveillance and Response, World Health
ORGANIZATION, 2003 Geneva, Severe Acute Respiratory Syndrome
(SARS): Status of the outbreak and lessons for the immediate future.
[2] CDC (Center of Disease Control) (2003). Update: Outbreak of Severe
Acute Respiratory SyndromeÔÇöWorldwide, 2003, MMWR 52(12), 241.
[3] CDC (Center of Disease Control) Basic Information About SARS.
Website http://www.cdc.gov/ncidod/ sars/factsheet.htm 16th April.
[4] Riley S, Fraser C, Donnelly CA, Ghani AC, Abu-Raddad LJ, Hedley
AJ, Leung GM, Ho LM, Lam TH, Thach TQ, Chau P, Chan KP, Lo SV,
Leung PY, Tsang T, Ho W, Lee KH, Lau EMC, Ferguson NM,
Anderson RM, (2003), Transmission Dynamics of the Etiological
Agent of SARA in Hong Kong: Impact of Public Health Interventions.
Science 300, 1961.
[5] Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L,
Gopalakrishna G, Chew SK, Tan, CC, Samore MH, Fishman D, Murray
M, (2003), Transmission Dynamics and Control of Severe Acute
Respiratory Syndrome. Science 300, 1966.
[6] Chowell G, Fenimore PW, Castillo-Garsow MA, Castillo-Chavex,
(2003, SARS outbreaks in Ontario, Hong Kong and Singapore: the role
diagnosis and isolation as a control mechanism. J. Theor. Biol. 224, 1
[7] Nishiura H, Patanarapelet K, Sriprom M, Sarakorn W. Sriyab S, Tang,
IM, (2004), Modeling potential responses to severe acute respiratory
syndrome in Japan: role of initial attack size, precaution and quarantine,
J. Epidemiol. Community Health 58, 186.
[8] Evans ND, White LJ, Chapman MJ, (2005), Math. Biosc. 194, 175.
[9] Storn R, Price K, (2004), Differential evolution web site of Storn and
Price as of August, 2004,
http://www.icsi.berkeley.edu/~storn/code.html.
[10] Laird AK, (1964), Dynamics of tumor growth : Comparison of growth
rates and extrapolation of growth curve of one cell, Br. J. Cancer 19,
278.
[11] Kermack WO, McKendrick AO, (1927), A contribution to the
mathematical theory of Epidemicc.bvProc. R. Soc. A115, 700.
[12] Storn R, Price K, (996), Minimizing the real functions of the ICEC- 96
cntest by Differetial Evolution., IEEE Conf. on Evolutionary
Computation. Nagoya, 1996, p. 842.
[13] Lopez CH, van Willigenburg, Van Straten G, (2000), Evolutionary
Algorith foroptimal control of chemical
processes., Proc. Of the IASTED International Conf. Control & Applic.
(CA200. (ed. Hamza MH) May 24-27
(2000) a Jolla, CA. USA.
[14] Gammaltoni L, Nucci MC, (1997), Using a mathematical model to
evaluate the efficacy of TB control measures., EID 3, 335.
[15] Barth-Jones DC, Longini IM, (2002), Determininbg optimal
vaccination policy for HIV vaccines: A dynamic simulation model for
the evaluation of vaciination policy. Proc. Of the International Conf.
on health science simulation 2002, (ed. Anderson JG, Katzper M) Jan.
27-31, 2002. San Antonia, Texas.
[16] Bowman C, Gumel AB, ven den Driesche, Wu J, Zhu H, (2005), A
mathematical model for assessing control strategies against West Nile
virus. Bull. Math. Biol. 67, 1107.
[1] Communicable Disease Surveillance and Response, World Health
ORGANIZATION, 2003 Geneva, Severe Acute Respiratory Syndrome
(SARS): Status of the outbreak and lessons for the immediate future.
[2] CDC (Center of Disease Control) (2003). Update: Outbreak of Severe
Acute Respiratory SyndromeÔÇöWorldwide, 2003, MMWR 52(12), 241.
[3] CDC (Center of Disease Control) Basic Information About SARS.
Website http://www.cdc.gov/ncidod/ sars/factsheet.htm 16th April.
[4] Riley S, Fraser C, Donnelly CA, Ghani AC, Abu-Raddad LJ, Hedley
AJ, Leung GM, Ho LM, Lam TH, Thach TQ, Chau P, Chan KP, Lo SV,
Leung PY, Tsang T, Ho W, Lee KH, Lau EMC, Ferguson NM,
Anderson RM, (2003), Transmission Dynamics of the Etiological
Agent of SARA in Hong Kong: Impact of Public Health Interventions.
Science 300, 1961.
[5] Lipsitch M, Cohen T, Cooper B, Robins JM, Ma S, James L,
Gopalakrishna G, Chew SK, Tan, CC, Samore MH, Fishman D, Murray
M, (2003), Transmission Dynamics and Control of Severe Acute
Respiratory Syndrome. Science 300, 1966.
[6] Chowell G, Fenimore PW, Castillo-Garsow MA, Castillo-Chavex,
(2003, SARS outbreaks in Ontario, Hong Kong and Singapore: the role
diagnosis and isolation as a control mechanism. J. Theor. Biol. 224, 1
[7] Nishiura H, Patanarapelet K, Sriprom M, Sarakorn W. Sriyab S, Tang,
IM, (2004), Modeling potential responses to severe acute respiratory
syndrome in Japan: role of initial attack size, precaution and quarantine,
J. Epidemiol. Community Health 58, 186.
[8] Evans ND, White LJ, Chapman MJ, (2005), Math. Biosc. 194, 175.
[9] Storn R, Price K, (2004), Differential evolution web site of Storn and
Price as of August, 2004,
http://www.icsi.berkeley.edu/~storn/code.html.
[10] Laird AK, (1964), Dynamics of tumor growth : Comparison of growth
rates and extrapolation of growth curve of one cell, Br. J. Cancer 19,
278.
[11] Kermack WO, McKendrick AO, (1927), A contribution to the
mathematical theory of Epidemicc.bvProc. R. Soc. A115, 700.
[12] Storn R, Price K, (996), Minimizing the real functions of the ICEC- 96
cntest by Differetial Evolution., IEEE Conf. on Evolutionary
Computation. Nagoya, 1996, p. 842.
[13] Lopez CH, van Willigenburg, Van Straten G, (2000), Evolutionary
Algorith foroptimal control of chemical
processes., Proc. Of the IASTED International Conf. Control & Applic.
(CA200. (ed. Hamza MH) May 24-27
(2000) a Jolla, CA. USA.
[14] Gammaltoni L, Nucci MC, (1997), Using a mathematical model to
evaluate the efficacy of TB control measures., EID 3, 335.
[15] Barth-Jones DC, Longini IM, (2002), Determininbg optimal
vaccination policy for HIV vaccines: A dynamic simulation model for
the evaluation of vaciination policy. Proc. Of the International Conf.
on health science simulation 2002, (ed. Anderson JG, Katzper M) Jan.
27-31, 2002. San Antonia, Texas.
[16] Bowman C, Gumel AB, ven den Driesche, Wu J, Zhu H, (2005), A
mathematical model for assessing control strategies against West Nile
virus. Bull. Math. Biol. 67, 1107.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:63855", author = "Weerachi Sarakorn and I-Ming Tang", title = "No one Set of Parameter Values Can Simulate the Epidemics Due to SARS Occurring at Different Localities", abstract = "A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.
", keywords = "SARS, mathematical modelling, differential evolution algorithm.", volume = "1", number = "10", pages = "502-6", }
