A simple approximate mathematical model to predict the number of severe acute respiratory syndrome cases and deaths

. . Background: Severe acute respiratory syndrome (SARS) is currently spreading in many countries. This paper proposes a simple approximate mathematical model for public health practitioners to predict the number of SARS cases and deaths. Methods: The model is based on four parameters: R o (basic reproductive number), F (case-fatality rate), i (incubation period), and d (duration of disease). The calculations can be done by hand or by using a computer spreadsheet. Results: The best parameters to fit Canadian data as of 6 April 2003 (before infection controls took effect) are R o = 1.5, F = 30%, i = 5 days, d = 14 days. On 6 April (day 40) there were 74 cases and 7 deaths. If this trend continues, SARS numbers in Canada are predicted to be as follows: 387 cases and 34 deaths by 26 April (day 60), 4432 cases and 394 deaths by 26 May (day 90), and 50 500 cases and 4489 deaths by 25 June (day 120). By comparison, the best parameters to fit Hong Kong data as of 10 April 2003 are R o = 2.0, F = 20%, i = 5 days, d = 14 days. Conclusions: Using the proposed mathematical model, it was estimated that about 1.5 to 2 new infectious cases were produced per infectious case every five days. Also, about 20% to 30% of the cases die within 14 days. The case-fatality may therefore be considerably higher than initially thought. The model indicates that SARS can spread very fast when there are no interventions.

[1]  William McGuire,et al.  Epidemiology of preterm birth , 2004, BMJ : British Medical Journal.

[2]  S. Selvin,et al.  Preterm birth among African American and white women: a multilevel analysis of socioeconomic characteristics and cigarette smoking , 2003, Journal of epidemiology and community health.

[3]  V. Grech,et al.  Seasonality of live birth sex ratio in south western Siberia, Russia, 1959–2001 , 2003, Journal of epidemiology and community health.

[4]  C. Fraser,et al.  Epidemiological determinants of spread of causal agent of severe acute respiratory syndrome in Hong Kong , 2003, The Lancet.

[5]  H. Becher,et al.  SARS, lay epidemiology, and fear , 2003, The Lancet.

[6]  Christian Drosten,et al.  Identification of a novel coronavirus in patients with severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[7]  Arthur S Slutsky,et al.  Identification of severe acute respiratory syndrome in Canada. , 2003, The New England journal of medicine.

[8]  J. Gerberding.  Faster... but fast enough? Responding to the epidemic of severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[9]  Peter Cameron,et al.  A major outbreak of severe acute respiratory syndrome in Hong Kong. , 2003, The New England journal of medicine.

[10]  J. A. Comer,et al.  A novel coronavirus associated with severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[11]  M. Chan-yeung,et al.  A cluster of cases of severe acute respiratory syndrome in Hong Kong. , 2003, The New England journal of medicine.

[12]  J. Drazen.  Case clusters of the severe acute respiratory syndrome. , 2003, The New England journal of medicine.

[13]  C. DesRoches,et al.  Common concerns amid diverse systems: health care experiences in five countries. , 2003, Health affairs.

[14]  U. Reinhardt,et al.  It's the prices, stupid: why the United States is so different from other countries. , 2003, Health affairs.

[15]  E. Walsh,et al.  Novel coronavirus and severe acute respiratory syndrome , 2003, The Lancet.

[16]  Y. Guan,et al.  Coronavirus as a possible cause of severe acute respiratory syndrome , 2003, The Lancet.

[17]  G. Zielhuis,et al.  The secular trends in male:female ratio at birth in postwar industrialized countries. , 2001, Environmental health perspectives.

[18]  D. Whiteis,et al.  The Social Health of the Nation: How America is Really Doing , 2000 .

[19]  M. Bracken,et al.  Intergenerational effects of high socioeconomic status on low birthweight and preterm birth in African Americans. , 2000, Journal of the National Medical Association.

[20]  H. Wilson,et al.  Rates of and factors associated with recurrence of preterm delivery. , 2000, JAMA.

[21]  T. Vartiainen,et al.  Environmental chemicals and changes in sex ratio: analysis over 250 years in finland. , 1999, Environmental health perspectives.

[22]  A. Lerchl.  Sex Ratios at Birth and Environmental Temperatures , 1999, Naturwissenschaften.

[23]  K. Fiscella,et al.  Racial disparities in preterm births. The role of urogenital infections. , 1996, Public health reports.

[24]  G. Smith,et al.  Basic Epidemiology , 1994 .

[25]  P. Kaye.  Infectious diseases of humans: Dynamics and control , 1993 .

[26]  K. Hatfield-Timajchy,et al.  Preterm delivery among African-American women: a research strategy. , 1993, American journal of preventive medicine.

[27]  H. Hansluwka.  Measuring health. A review of quality of life measurement scales: by Ann Bowling , 1992 .

[28]  N. Mantel,et al.  Socio-economic factors and the sex ratio at birth , 1971, Journal of Biosocial Science.

[29]  Frank Sandon,et al.  Season of birth: its relation to human abilities , 1939 .

[30]  P. Jongbloet.  A challenging hypothesis for sex ratio modulation , 2004 .

[31]  Manfred Huber,et al.  Health Expenditure Trends in OECD Countries, 1970-1997 , 1999, Health care financing review.