1. R E 1 Uncovering the contact networks behind emerging epidemics of respiratory spread agents Jacco Wallinga

2. r contact patterns | jacco.wallinga@rivm.nl Respiratory spread infectious agents endemic respiratory infections (influenza, tuberculosis, etc) are responsible for 11% of all deaths world-wide potentially pandemic respiratory infections (new influenza strains, smallpox, SARS) can cause many more deaths transmission primarily through small infectious droplets, dispersed over a short range

3. r contact patterns | jacco.wallinga@rivm.nl Description of the “respiratory spread” transmission route in epidemic models mathematically convenient a-priori assumption –random mixing –proportionate mixing –ad-hoc

4. r contact patterns | jacco.wallinga@rivm.nl Description of the “respiratory spread” transmission route by contact networks nodeindividual edgecontact between individuals degreenumber of contacts per individual degree distributionprobability distribution for degree

5. r contact patterns | jacco.wallinga@rivm.nl What is contact? (1) infectious contact –unobservable event –directed (John infects Mary, Mary does not infect John)

6. r contact patterns | jacco.wallinga@rivm.nl Infectious contacts (SARS in Singapore 2003) MMWR 2003; 52: 405

7. r contact patterns | jacco.wallinga@rivm.nl What is contact? (2) social contact as a proxy measure of infectious contacts –e.g. having at least one conversation during a week –e.g. being at the same location during at least one hour –undirected (John contacts Mary, Mary contacts John)

8. r contact patterns | jacco.wallinga@rivm.nl Social contacts (being in the same location) Eubank et al (2004) Nature; 429: 180-184

9. r contact patterns | jacco.wallinga@rivm.nl Uncovering networks for respiratory spread agents involves Testing the validity of proxy measures –Proxy measure: having at least one conversation during a week –Test on age-specific seroprevalence against mumps –Test on age-specific attack rates of Asian flu Inferring infectious contacts from epidemic outbreaks –Transmission tree from SARS outbreaks –Transmission tree from smallpox outbreaks Uncovering the contact networks behind emerging epidemics

10. r contact patterns | jacco.wallinga@rivm.nl Testing the validity of proxy measures

11. r contact patterns | jacco.wallinga@rivm.nl Conversation as a proxy measure Ask people to record their age and the age of individuals they talk to during the day is it a valid proxy measure of infectious contacts? Edmunds et al. Proc R Soc Lond B 1997; 264: 949-957

12. r contact patterns | jacco.wallinga@rivm.nl Proxy measures for contact networks… social contact: at least one conversation during a week undirected edges (John contacts Mary, Mary contacts John) degree of a node: number of social contacts from individual in age class j with others in age class i degree distribution is negative binomial –mean m ij –variance m ij + m ij 2 / k ij

13. r contact patterns | jacco.wallinga@rivm.nl …and the infectious contact network itself infectious contact: transmission from one to the other directed edges (John infects Mary, Mary did not infect John) outdegree of a node: number of infectious contacts produced by individual in age class j to others in age class i outdegree distribution is negative binomial –mean n ij –variance n ij + n ij 2 / k ij

14. r contact patterns | jacco.wallinga@rivm.nl The hypothesis age distribution of number of infectious contacts per individual is proportional to age distribution of number of social contacts per individual (that is, n ij = q m ij ) alternatives –age distribution of number of infectious contacts per individual reflects age distribution of population (random mixing) –age distribution of number of infectious contacts per individual reflects an age-specific activity level (proportionate mixing)

15. r contact patterns | jacco.wallinga@rivm.nl Data large cross-sectional study in Utrecht, 1986 1813 participants reported on their contact behaviour –number of different persons in the household –number of different persons conversed with during a week 1859 participants were screened for mumps-specific antibodies

16. r contact patterns | jacco.wallinga@rivm.nl Age-specific degree distribution

17. r contact patterns | jacco.wallinga@rivm.nl Fit to age-stratified prevalence of mumps- specific antibodies (Netherlands, 1986)

18. r contact patterns | jacco.wallinga@rivm.nl Validation against mumps serological data

19. r contact patterns | jacco.wallinga@rivm.nl Data large household study in Cleveland, 1950’s household members provided serum over time serum was screened for antibodies specific to the 1957 ‘Asian’ influenza pandemic –128 unvaccinated participants younger than 20 years –fourfold or larger rise in antibody level during the first pandemic wave indicates infection –Jordan et al. Am J Hyg 1958; 68: 190-212

20. r contact patterns | jacco.wallinga@rivm.nl Fit to age-stratified prevalence of antibodies after the Asian flu pandemic (USA, 1957)

21. r contact patterns | jacco.wallinga@rivm.nl Validation against influenza serological data

22. r contact patterns | jacco.wallinga@rivm.nl Having a conversation is a valid proxy measure of infectious contacts for respiratory diseases avoid a-priori assumptions such as random or proportionate mixing even though conversation events may resemble transmission events, no causal relation is implied

23. r contact patterns | jacco.wallinga@rivm.nl Inferring infectious contacts from epidemic outbreaks

24. r contact patterns | jacco.wallinga@rivm.nl Inferring infectious contacts Some epidemiologic links between cases are observed Impute missing links to reconstruct transmission trees is this a statistically sound approach? Haydon et al. Proc R Soc Lond B 2002; 270: 121-127

25. r contact patterns | jacco.wallinga@rivm.nl Likelihood-based inference procedure for transmission trees basic idea: –estimate the likelihood of all possible transmission trees requires the following assumptions: –all cases are known –all infectious contacts are independent (that is, all cases are considered equally infectious) –generation interval is known and has a stationary distribution

26. r contact patterns | jacco.wallinga@rivm.nl Notation The epidemic is described as a directed graph with n nodes (cases) and n-q directed links (transmission events) Each node has exactly one incoming link The nodes are labeled by an index i {1,...,n} Each network is represented by a vector v of length n, where the i th element v(i) gives the label of the infector of case i Times of symptom onset are given by a vector t of length n t i - t v(i) is denoted by  Probability density function is w(  |  ); w(  |  )=0 for  < 0.

27. r contact patterns | jacco.wallinga@rivm.nl Likelihood of networks The likelihood for one network v, given observed times of symptom onset t The likelihood of all networks V, given observed times of symptom onset t The likelihood of all networks V, given that case k has been infected by case l

28. r contact patterns | jacco.wallinga@rivm.nl Estimation of reproduction numbers relative likelihood that case k has been infected by case l expected value of number of secondary cases for case l With approximate distribution

29. r contact patterns | jacco.wallinga@rivm.nl Example: outbreaks of Severe Acute Respiratory Syndrome (SARS) in 2003 infectious agent: SARS coronavirus over 900 deaths in 2003 over 8,400 cases in 2003

30. r contact patterns | jacco.wallinga@rivm.nl Methods: epidemic curve List with values t i, date of onset of symptoms of the i th case

31. r contact patterns | jacco.wallinga@rivm.nl Methods: generation interval the generation interval, , is the duration between onset of symptoms of a secondary case and its primary case distribution of  can be described by a Weibull distribution w (  |  )

32. r contact patterns | jacco.wallinga@rivm.nl Methods: from epidemic curve to reproduction number Likelihood of case i being infected by case j Probability of case i being infected by case j Number of secondary cases attributable to case j

33. r contact patterns | jacco.wallinga@rivm.nl Results Daynumber in 2003 Number of cases R SingaporeCanada

34. r contact patterns | jacco.wallinga@rivm.nl Results Daynumber (since start of outbreak) Canada

35. r contact patterns | jacco.wallinga@rivm.nl Example: smallpox outbreak in 1951 Intervention measures during a smallpox outbreak in the Netherlands, in 1951 –In the town of Tilburg –123 000 inhabitants –50 cases of smallpox

36. r contact patterns | jacco.wallinga@rivm.nl Epidemic curve of the 1951 smallpox outbreak 27 February 1951: –symptom onset of the first case 30 April 1951: control –All patients are moved to a single hospital –All their contacts are vaccinated and quarantined for 18 days –All children younger than 1 year are vaccinated –All vaccinated individuals in Tilburg are revaccinated 25 May 1951: –symptom onset of the last case

37. r contact patterns | jacco.wallinga@rivm.nl Notation for the generation interval the generation interval, , is the duration between onset of symptoms of a secondary case and its primary case distribution of  can be described by a Log Normal distribution g (  |  )

38. r contact patterns | jacco.wallinga@rivm.nl Estimation of a transmission tree Some links are observed Some links are missing Use standard missing data techniques to estimate missing links, based on symptom onset dates of nodes

39. r contact patterns | jacco.wallinga@rivm.nl Results transmission tree reproduction numbers epidemic curve

40. r contact patterns | jacco.wallinga@rivm.nl Transmission trees can be inferred from the observed epidemic curve capture information about reproduction numbers, generation intervals cannot capture information about exposure of individuals that are either infected or immune

41. r contact patterns | jacco.wallinga@rivm.nl Uncovering contact networks behind emerging epidemics

42. r contact patterns | jacco.wallinga@rivm.nl The role of transmission trees in uncovering contact networks A transmission tree represents a causal model for the observed epidemic If we would rerun the epidemic, other transmission trees could represent causal models for these alternative (counterfactual) epidemics If we would have used alternative control measures, still other transmission trees could represent causal models for these alternative (counterfactual) epidemics The contact network captures the set of all actual and counterfactual transmission trees

43. r contact patterns | jacco.wallinga@rivm.nl The role of proxy measures in uncovering contact networks Proxy measures of infectious contacts help to identify the possible (counterfactual) infectious contacts that make up the alternative (counterfactual) transmission trees

44. r contact patterns | jacco.wallinga@rivm.nl What are contact networks? Set of contacts between individuals that includes –infectious contacts if an epidemic occurs among those individuals –possible (counterfactual) infectious contacts if we would rerun this epidemic –possible (counterfactual) infectious contacts if we would have used alternative control measures

45. r contact patterns | jacco.wallinga@rivm.nl Why one should be interested in uncovering contact networks for emerging epidemics Uncovering a contact network is essential whenever we require counterfactual outcomes of epidemics –if we estimate the effectiveness of implemented control measures, we compare the actual outcome (with control) with the counterfactual outcome (without control) Control of emerging epidemics requires insight in the effectiveness of possible control measures Any measure of effectiveness implies an assumption about the contact network –this assumptions should be made explicit –and held up against available evidence

46. r contact patterns | jacco.wallinga@rivm.nl Acknowledgements School of Public Health, Bielefeld University, Germany –Mirjam Kretzschmar Center for Statistics, Hasselt University, Belgium –Han Ling Harvard School of Public Health, USA –Eben Kenah, Jamie Robins, Marc Lipsitch National Institute for Public Health and the Environment, Bilthoven, the Netherlands –Peter Teunis –Siem Heisterkamp –Nico Nagelkerke

47. r contact patterns | jacco.wallinga@rivm.nl References Wallinga J, Edmunds WJ, Kretzschmar M. Human contact patterns and the spread of airborne infectious diseases. Trends in Microbiology 7: 372-377 (1999) Wallinga J, Teunis P. Different epidemic curves for Severe Acute Respiratory Syndrome reveal similar impacts of control measures. American Journal of Epidemiology 160: 509-516 (2004). Wallinga J, Teunis P, Kretzschmar M. Using social contact data to estimate age-specific transmission parameters for infectious respiratory spread agents. American Journal of Epidemiology (conditionally accepted).

48. r contact patterns | jacco.wallinga@rivm.nl