Testing Different Spatial Kernels

Unravelling transmission trees of infectious diseases by combining genetic and epidemiological data

R.J.F. Ypma1,2*, A.M.A. Bataille3,4, A. Stegeman3, G. Koch4, J. Wallinga1,2, W.M. van

Ballegooijen1

1 National Institute of Public Health and the Environment, Bilthoven, the Netherlands 2 Julius Centre for Health Research and Primary Care, University Medical Centre Utrecht, the Netherlands 3 Department of Farm Animal Health, Faculty of Veterinary Medicine, Utrecht University, Utrecht, the Netherlands 4 Department of Virology, Central Veterinary Institute, Animal Sciences Group, Wageningen University and Research Centre, Lelystad, the Netherlands * Corresponding author; Email address: [email protected]

Supplementary Materials

Representing the transmission tree

A graphical representation of the estimated transmission tree was given in the main text (figure 2). To increase clarity for the area with highest farm-density, figure S1 gives a zoomed-in version of figure 2 for this area.

Testing different spatial kernels

The form of the spatial kernel used in the main text was taken from Boender et al. [1], who tested a number of parameterisations and found this kernel to fir the data best. To see whether this choice of parametric form influences our results, we test a range of kernels found in the literature (table S1, second column). The first five kernels tested are taken from Boender et al. [1], where kernel 5 is the kernel from the main article, and kernel 1 is identical to the analysis given in the main text using only genetic and temporal data. Kernels 6-8 are from a family of kernels featuring an exponential decay term. These have for instance been used for modelling the spread of foot-and- mouth disease [2, 3] and the dispersal of plant seeds [4, 5]. To calculate the effect of using different kernels, we substitute them in equation (3) in the main text, and rerun the analysis.

Table S1 gives estimates of parameter values for all kernels tested, figure S2 gives the resolution of the estimated trees (comparable to figure 3 in the main text) and figure S3 gives the estimated average infectiousness of different types of farms

(comparable to figure 5 in the main text).

We see that, although analyses using different kernels result in different values for the probabilities of transmissions, the results on resolution of the tree and infectiousness of farm types remain the same. Resolution is slightly lower for kernels

1 and 6. The first is the analysis without geographical data, the second comes close to this analysis since its two parameters are both estimated to be very close to zero (table

S1). These parameters c and d in the exponential decay factor are consistently estimated very low, which is an indication that the exponential decaying function does not fit this epidemic well. The high estimated value for d in kernel 7 is probably due to very low estimates for c. Estimates of parameter values for genetic and temporal parameters are robust for different spatial kernels (table S2), which is probably due to the relatively low amount of information contained in the geographical data (main text). Table S1 Spatial parameter estimates for models with different spatial kernels

Spatial kernel α (95% CI) r0 (95% CI) c (95% CI) d (95% CI) 1 1 - - - - 2 (1+x)-1 - - - - 3 (1+x2)-1 - - - - 4 (1+xα)-1 1.7 (1.5, 2.0) - - - α -1 5 (1+(x/r0) ) 2.3 (1.7, 2.8) 2.4 (1.2, 3.7) - - 6 exp(-c xd) - - 0.039 (0.00075, 0.65) 0.12 (0.00087, 1.2) 7 (1+xα)-1 2.3 (1.7, 2.9) - 0.046 (0.0037, 0.13) 10 (4.0, 13) exp(-c xd) α -1 8 (1+(x/r0) ) 2.4 (1.8, 3.1) 2.3 (1.3, 4.7) 0.14 (0.0051, 0.71) 0.46 (0.0064, 2.3) exp(-c xd)

Table S2 Temporal and genetic parameter estimates for models with different spatial

kernels Spatial kernel b (95% CI) pts (95% CI) ptv (95% CI) pdel (95% CI) 1 1 0.25 (0.20, 0.31) 1.1 (0.86, 1.3) 0.30 (0.20, 0.41) 0.060 (0.028, 0.11) 2 (1+x)-1 0.28 (0.22, 0.35) 1.1 (0.88, 1.3) 0.31 (0.22, 0.42) 0.063 (0.031, 0.11) 3 (1+x2)-1 0.29 (0.24, 0.35) 1.1 (0.89, 1.3) 0.32 (0.22, 0.42) 0.068 (0.030, 0.12) 4 (1+xα)-1 0.29 (0.23, 0.35) 1.1 (0.88, 1.3) 0.31 (0.21, 0.41) 0.066 (0.029, 0.12) α -1 5 (1+(x/r0) ) 0.28 (0.23, 0.34) 1.1 (0.88, 1.3) 0.32 (0.22,0.43) 0.069 (0.027, 0.13) 6 exp(-c xd) 0.24 (0.20, 0.30) 1.1 (0.87, 1.3) 0.30 (0.20, 0.41) 0.063 (0.029, 0.12) (1+xα)-1 7 0.29 (0.23, 0.35) 1.1 (0.89, 1.3) 0.31 (0.22, 0.42) 0.068 (0.031, 011) exp(-c xd) α -1 (1+(x/r0) ) 8 0.28 (0.23, 0.34) 1.1 (0.88, 1.3) 0.31 (0.22, 0.42) 0.066 (0.030, 0.12) exp(-c xd)

Another possibility is to use distance over road rather than Euclidean distance

as a measure for geographical distance, such as done for foot and mouth disease by

Savill et al. [6]. Unfortunately we lack the data to do this analysis thoroughly; to our

knowledge there is no extensive database containing all (minor) roads in the particular

area. However, we believe the analysis would yield results similar to the one we

performed using Euclidean distance, as this is a very road-dense area with no large

geographical obstacles. Furthermore it is quite likely that several different

mechanisms were responsible for spread of the disease, some following the road- and

others the Euclidean distance. For FMD this mixture of transmission mechanisms was given as a possible explanation for the fact that Euclidean distance gave the better fit, unless a geographical obstacle was present [6].

Latent period

Although the assumption of a latent period seems valid for the avian influenza epidemic [7-9], the exact length for this latent period is not known. In the main article we assumed a length of one day; here we test this assumption for robustness. We do this by increasing the length of the latent period in equation (1) in the main text, and rerunning the full analysis.

Table S3 gives estimates of parameter values for the different analyses, figure

S4 gives the resolution of the estimated trees (comparable to figure 3 in the main text) and S5 gives the estimated average infectiousness of different types of farms

(comparable to figure 5 in the main text).

Although analyses using different latent periods result in different values for the probabilities of transmissions, the estimates of parameter values as well as the resolution of the tree remain the same. Estimates of infectiousness of farm types vary slightly, especially for the types that included fewer farms. This is probably due to the fact that some transmissions become impossible in the model when the latent period is increased, which can have a large impact on the average infectiousness of a small group of farms. However all conclusions remain unchanged. Table S3 Comparison between models with different length of latent period

Length of latent b (95% CI) α (95% CI) r0 (95% CI) pts (95% CI) ptv (95% CI) pdel (95% CI) period (days) 1 0.28 (0.23, 0.34) 2.3 (1.7, 2.8) 2.4 (1.2, 3.7) 1.1 (0.88, 1.3) 0.32 (0.22,0.43) 0.069 (0.027, 0.13) 2 0.29 (0.24, 0.35) 2.3 (1.8, 2.9) 2.4 (1.3, 3.9) 1.1 (0.91, 1.4) 0.30 (0.21, 0.42) 0.074 (0.034, 0.12) 3 0.22 (0.18, 0.26) 2.4 (2.0, 3.0) 2.4 (1.5, 3.5) 1.2 (1.0, 1.5) 0.33 (0.24, 0.45) 0.078 (0.040, 0.11) 1. Boender G.J., Hagenaars T.J., Bouma A., Nodelijk G., Elbers A.R., de Jong

M.C., van Boven M. 2007 Risk maps for the spread of highly pathogenic avian influenza in poultry. PLoS Comput. Biol. 3, e71. (doi: 10.1371/journal.pcbi.0030071)

2. Ferguson N. M., Donnelly C.A., Anderson R.M. 2001 The Foot-and-Mouth

Epidemic in Great Britain: Pattern of Spread and Impact of Interventions. Science

292, 1155-1160.

3. Thornley J.H.M., France J. 2009 Modelling foot and mouth disease. Prev. Vet.

Med. 89, 139-154

4. Portnoy S., Willson M.F. 1993 Seed dispersel curves: behaviour of the tail of the distribution. Evolutionary Ecology 7, 25-44.

5. Shaw M.W., Harwood T.D., Wilkinson M.J., Elliot L. 2006 Assembling spatially explicit landscape models of pollen and spore dispersal by wind for risk assessment. Proc. R. Soc. B 273, 1705-1713

6. Savill N.J., Shaw D.J., Deardon R., Tildesley M.J., Keeling M.J., Woolhouse

M.E.J., Brooks S.P., Grenfell B.T. 2006 Topographic determinants of foot and mouth disease transmission in the UK 2001 epidemic. BMC Veterinary Research 2:3. (doi:

10.1186/1746-6148-2-3)

7. Bos M.E., van Boven M., Nielen M., Bouma A., Elbers A.R., Nodelijk G.,

Koch G., Stegeman A., de Jong M.C. 2007 Estimating the day of highly pathogenic avian influenza (H7N7) virus introduction into a poultry flock based on mortality data. Vet. Res. 38, 493-504. (doi: 10.1051/vetres:2007008)

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9. Spekreijse D., Bouma A., Stegeman J.A. , Koch G., de Jong M.C.M. 2010 The effect of inoculation dose of a highly pathogenic avian influenza virus strain H5N1 on the infectiousness of chickens. Veterinary Microbiology. 147 (1-2), 59-66. (doi:

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Figure S1. Infection events with posterior probability >0.5, in the northern part of the outbreak. This is a zoomed-in version of figure 2 in the main text. Results are for a model using (a) temporal, genetic and geographic, and (b) temporal and genetic data.

Red dots denote infected farms, yellow dots denote farms not infected in the epidemic. A higher opacity of arrows corresponds to a higher estimated probability.

We see the two analyses give roughly the same transmission links, although the addition of geographic data allows for more precise estimations. Figure S2. Resolution of the estimated trees, using different spatial kernels. For each level of probability, the percentage of farms for which the farm that infected it can be estimated at or above this level is plotted. Kernels 1-8 (table S1) are coloured blue, yellow, orange, grey, black, cyan, magenta and brown respectively. Kernels 5 and 1

(black and blue) are the analyses from the main text using all data and only using genetic and temporal data. Striped and dotted lines give the same information for sequenced and unsequenced farms respectively. All trees have roughly the same resolution, apart from those resulting from kernels 1 and 6 (blue and cyan lines). The former uses no spatial information, while the latter comes close to this analysis since the kernel solely consists of an exponential decrease, whose parameters have been estimated close to zero. This is an indication exponential decay does not fit this data well. Figure S3. Estimated average infectiousness for different types of farms, as measured by number of infections caused divided by the time period in days between infection and culling of the farm. Results are for models using different spatial kernels, kernels

1-8 (table S1) are coloured blue, yellow, orange, grey, black, cyan, magenta and brown respectively. Kernels 5 and 1 (black and blue) are the analyses from the main text using all data and only using genetic and temporal data. Estimates are similar for all kernels, kernels 1 and 6 (blue and cyan) have less discriminatory power and therefore less variation in their estimates. Figure S4. Resolution of the estimated trees, assuming the latent period is one (black), two (orange) or three (red) days. For each level of probability, the percentage of farms for which the farm that infected it can be estimated at or above this level is plotted.

Striped and dotted lines give the same information for sequenced and unsequenced farms respectively. All trees have roughly the same resolution. Figure S5. Estimated average infectiousness for different types of farms, as measured by number of infections caused divided by the time period in days between infection and culling of the farm. Results are for models using a latent period of one (black), two (orange) or three (red) days. We can see some small differences, especially for duck farms. This is probably because some transmissions become impossible in the model when a longer latent period is assumed. However the conclusions of low infectiousness of hobby farms and high infectiousness of turkey farms remain unaltered.