Abstract
An estimate of the interval between successive infections is essential for surveillance, control, and modeling of infectious diseases. This paper proposes a method for determining the serial interval when the location and time of onset of illness are known. The theoretical underpinning of this method is the intrinsically spatial nature of disease transmission. Successive infections tend to be closer than unrelated cases of disease and, therefore, exhibit spatial clustering. An incremental Knox type analysis of cases is introduced. Cases occurring at a range of time intervals are examined to determine the serial interval. The significance of clustering is determined using a permutation approach under the null hypothesis of space-time independence. The power of this method is evaluated using an individual level, spatially explicit epidemic simulation. The time increment Knox test is robust to multiple introductions and incomplete sampling. Finally, the increment Knox statistic is used to analyze an outbreak of dengue fever in the city of Florida, Puerto Rico during 1991. Results indicate that the likely interval between successive cases during this outbreak is at least 18–19 days.
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References
Anderson RM, May RM (1991) Infectious diseases of humans: dynamics and control. Oxford University Press, Oxford
Bailey NTJ (1975) The mathematical theory of infectious disease and its applications. Charles Griffin & Company Ltd, London
Baker RD (1996) Testing for space-time clusters of unknown size. J Appl Stat 23:543–554
Barton DE, David FN (1966) The random intersection of two graphs. In: David FN (ed) Research papers in statistics, Festschrift for J. Neyman. Wiley, New York, pp 445–459
Bian L (2004) A conceptual framework for an individual-based spatially explicit epidemiological model. Environ Plann B Plann Des 31:381–395
Cliff A, Haggett P (1982) Methods for the measurement of epidemic velocity from time-series data. Int J Epidemiol 11:82–89
Cliff AD, Haggett P, Ord JK, Versey GR (1981) Spatial diffusion: an historical geography of epidemics in an Island community. Cambridge University Press, Cambridge
Dever GEA (2006) Managerial epidemiology: practice, methods, and concepts. Jones and Bartlett Publishers, Sudbury, MA
Diggle P, Chetwynd A, Haggkvist R, Morris S (1995) Second-order analysis of space-time clustering. Stat Meth Med Res 4:124–136
Doyle TJ, Glynn MK, Groseclose SL (2002) Completeness of notifiable infectious disease reporting in the United States: an analytical literature review. Am J Epidemiol 155:866–974
Endy TP, Chunsuttiwat S, Nisalak A, Libraty DH, Green S, Rothman AL, Vaughn DW, Ennis FA (2002) Epidemiology of inapparent and symptomatic acute dengue virus infection: a prospective study of primary school children in Kampaeng Phet, Thailand. Am J Epidemiol 156:40–51
Etkind SC (1993) Contact tracing in tuberculosis. In: Reichman LB, Hershfield ES (eds) Tuberculosis: a comprehensive international approach. Marcel Dekker, Inc., New York, pp 275–289
Fine PEM (2003) the interval betwen successive cases of an infectious disease. Am J Epidemiol 158:1039–1047
Gubler DJ (1988) Dengue. In: Monath TP (ed) The arboviruses: epidemiology and ecology. CRC Press, Inc., Boca Raton, pp 223–260
Gubler DJ (1997a) Dengue and dengue hemorrhagic fever: its history and resurgence as a global public health problem. In: Gubler DJ, Kuno G (eds) Dengue and dengue hemorrhagic fever. CABI Publishing, Cambridge, pp 1–22
Gubler DJ (1997b) Epidemic dengue/dengue haemorrhagic fever: a global public health problem in the 21st century. In: W.M. Scheld DA, and J.M. Hughes (eds) Emerging Infections. ASM Press, Washington, DC, pp 1–14
Gubler DJ, Casta-Velez A (1991) A program for prevention and control of epidemic dengue and dengue hemorrhagic fever in Puerto Rico and the US Virgin Islands. Bull Pan Am Health Organ 25:237–247
Guha-Sapir D, Schimmer B (2005) Dengue fever: new paradigms for a changing epidemiology. Emerg Themes Epidemiol 2:1
Halstead SB (1997) Epidemiology of dengue and dengue hemorrhagic fever. In: Gubler DJ, Kuno G (eds) Dengue and dengue hemorrhagic fever. CABI Publishing, Cambridge, pp 23–44
Harrington LC, Buonaccorsi JP, Edman JD, Costero A, Kittayapong P, Clark GC, Scott TW (2001) Analysis of survival of young and old Aedes aegypti (Diptera: Culcidae) from Puerto Rico and Thailand. J Med Entomol 38:537–547
Holmes EC (1998) Molecular epidemiology of dengue virus—the time for big science. Trop Med Int Health 3:855–856
Hope Simpson RE (1952) Infectiousness of communicable diseases in the household. Lancet ii:549–554
Jacquez GM (1996) A k nearest neighbor test for space-time interaction. Stat Med 15:1935–1949
Knox EG (1964) Detection of space-time interactions. Appl Stat 13:25–29
Kulldorff M (2000) Prospective time periodic geographical disease surveillance using a scan statistic. J R Stat Soc A 164:61–72
Kulldorff M, Hjalmars U (1999) The Knox method and other tests for space-time interaction. Biometrics 55:544–552
Kuno G (1995) review of the factors modulating dengue transmission. Epidemiol Rev 17:321–335
Mantel N (1967) The detection of disease clustering and a generalized regression approach. Cancer Res 27:209–220
Meade MS, Earickson RJ (2000) Medical geography. The Guilford Press, New York
Morrison AC, Getis A, Santiago M, Rigau-Perez JG, Reiter P (1998) Exploratory disease analysis of reported dengue cases during an outbreak in Florida, Puerto Rico, 1991–1992. Am J Trop Hyg Med 58:287–298
Naus JI (1965) The distribution of the size of the maximum cluster of points on a line. J Am Stat Assoc 60:532–538
PAHO (1994) Dengue and dengue hemorrhagic fever in the Americas: Guidlines for prevention and control. PAHO, Washington, DC
Pickles WN (1939) Epidemiology in country practice. John Wright & Sons, Ltd., Bristol, England
Reiter P, Gubler DJ (1997) Surveillance and control of urban dengue vectors. In: Gubler DJ, Kuno G (eds) Dengue and dengue hemorrhagic fever. CAB International, New York, pp 425–462
Rodriguez-Figueroa L, Rigau-Perez JG, Suarez EL, Reiter P (1995) Risk factors for dengue infection during an outbreak in Yanes, Puerto Rico in 1991. Am J Trop Med Hyg 52:496–502
Samuelsson S, Ege P, Berthelsen L, Lind I (1992) An outbreak of serogroup B:15:P1.16 meningococcal disease, Frederiksborg county, Denmark, 1987–9. Epidemiol Infect 108:19–30
Scott TW, Chow E, Strickman D, Kittayapong P, Wurta R, Lorenz L, Edman JD (1993) Blood-feeding patterns of Aedes aegypti (Diptera: Culicidae) collected in a rural Thai village. J Med Entomol 30:922–927
Sheppard P, Macdonald W, Tonn R, Grab B (1969) The dynamics of an adult Aedes aegypti in relation to dengue hemorrhagic fever in Bangkok. J Anim Ecol 38:661–702
Small PM, Hopewell PC, Singh SP, Paz A, Parsonnet J, Ruston DC, Schecter GF, Daley CL, Schoolnik GK (1994) The epidemiology of tuberculosis in San Francisco—a population-based study using conventional and molecular methods. N Engl J Med 330:1703–1709
Tran A, Deparis X, Dussart P, Morvan J, Rabarison P, Remy F, Polidori L, Gardon J (2004) Dengue spatial and temporal patterns, French Guiana, 2001. Emerg Infect Dis 10:615–621
US Census Bureau (2000) PR-99-1 Estimates of the Population of Puerto Rico Municipios, July 1, 1999, and Demographic components of population change: April 1, 1990 to July 1, 1999. US Census Bureau, Washongton, DC
Vorndam V, Kuno G (1997) Laboratory diagnosis of dengue virus infections. In: Gubler DJ, Kuno G (eds) Dengue and dengue hemorrhagic fever. CAB International, Boca Raton, FL, pp 313–333
Ward MP, Carpenter TE (2000) Analysis of time-space clustering in veterinary epidemiology. Prev Vet Med 43:225–237
Watts D, Burke DS, Harrison BA, Whitmire RE, Nisalak A (1987) Effect of temperature on the vector efficiency of Aedes aegypti for dengue 2 virus. Am J Trop Hyg Med 36:143–152
Wearing HJ, Rohani P, Keeling MJ (2005) Appropriate models for the management of infectious diseases. PLOS Med 2:e174
WHO (2002) Fact sheet No.117, Dengue and dengue haemorrhagic fever. World Health Organization
Williams GW (1984) Time-space clustering of disease. In: Cornell RG (ed) Statistical methods for cancer studies. Marcel Dekker, Inc., New York, pp 167–228
Acknowledgments
I would like to express my appreciation for the funding provided by the National Institutes of Health (AI034533) and the National Science Foundation (BCS-0502020). I would especially like to thank Amy Morrison and Thomas W. Scott for providing the dengue case study data and comments on that portion of the manuscript. I would also like to thank Arthur Getis, Michael F. Goodchild, and two anonymous referees for their helpful comments.
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Aldstadt, J. An incremental Knox test for the determination of the serial interval between successive cases of an infectious disease. Stoch Environ Res Risk Assess 21, 487–500 (2007). https://doi.org/10.1007/s00477-007-0132-3
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DOI: https://doi.org/10.1007/s00477-007-0132-3