Figure 3: Suggested framework for incorporating contact structure (abundance and density data) into infectious disease models in ecologically informed ways. Whilst the framework is based on our particular bat–virus system, it should be broadly applicable, with minor modifications, to other systems. Suggestions for transmission structure are in grey. Continue the length of the decision tree for the full suggestion on transmission specification (i.e. to get combined scale and parameter choice). This framework is not exhaustive but instead aims to highlight the types of ecological questions that may be relevant for specifying contact structure within models. This framework assumes transmission is through direct contact. Note that this framework focusses on contact structure only as a driver of transmission, but other heterogeneities in the transmission process could exist (e.g. viral load and the probability of an individual becoming infected given an infective dose, see Lunnet al. (2019) and McCallum et al. (2017)).

References

Altizer, S., Dobson, A., Hosseini, P., Hudson, P., Pascual, M. & Rohani, P. (2006) Seasonality and the dynamics of infectious diseases.Ecology Letters, 9, 467-484.
Antonovics, J., Iwasa, Y. & Hassell, M.P. (1995) A generalized model of parasitoid, venereal, and vector-based transmission processes. The American Naturalist, 145, 661-675.
Baddeley, A. (2010) Analysing spatial point patterns in R. pp. 1-232. CSIRO.
Begon, M., Bennett, M., Bowers, R.G., French, N.P., Hazel, S. & Turner, J. (2002) A clarification of transmission terms in host-microparasite models: numbers, densities and areas. Epidemiology and Infection,129, 147-153.
Borremans, B., Reijniers, J., Hens, N. & Leirs, H. (2017) The shape of the contact–density function matters when modelling parasite transmission in fluctuating populations. Royal Society open science, 4, 171308.
Brandell, E.E., Becker, D.J., Sampson, L. & Forbes, K.M. (2020) The rise of disease ecology. bioRxiv .
Burnham, K.P. & Anderson, D.R. (2002) Model Selection and Multimodel Inference: a Practical Information-Theoretic Approach . Springer Science & Business Media, Fort Collins.
Clancy, T. & Einoder, L. (2004) Estimates of size of grey-headed flying-fox camp sites – evaluation of point transect using distance techniques. Arthur Rylah Institute for Environmental Research, Heidelberg, Victoria.
Colombi, D., Serra-Cobo, J., Métras, R., Apolloni, A., Poletto, C., López-Roig, M., Bourhy, H. & Colizza, V. (2019) Mechanisms for lyssavirus persistence in non-synanthropic bats in Europe: insights from a modeling study. Scientific Reports, 9, 1-11.
Cross, P.C., Caillaud, D. & Heisey, D.M. (2013) Underestimating the effects of spatial heterogeneity due to individual movement and spatial scale: infectious disease as an example. Landscape Ecology,28, 247-257.
Cross, P.C., Creech, T.G., Ebinger, M.R., Manlove, K., Irvine, K., Henningsen, J., Rogerson, J., Scurlock, B.M. & Creel, S. (2013) Female elk contacts are neither frequency nor density dependent.Ecology, 94, 2076-2086.
De Jong, M. (1995) Depend on Population Size? Epidemic models: their structure and relation to data (ed. D. Mollison), pp. 84. Cambridge University Press, Cambridge, United Kingdom.
De Jong, M.C.M. (2002) Modelling transmission: mass action and beyond - Response from McCallum, Barlow and Hone. Trends in Ecology & Evolution, 17, 64-65.
De Koeijer, A., Diekmann, O. & Reijnders, P. (1998) Modelling the spread of phocine distemper virus among harbour seals. Bulletin of Mathematical Biology, 60, 585-596.
Diggle, P. (1985) A kernel method for smoothing point process data.Journal of the Royal Statistical Society: Series C (Applied Statistics), 34, 138-147.
Epstein, J.H., Anthony, S.J., Islam, A., Kilpatrick, A.M., Ali Khan, S., Balkey, M.D., Ross, N., Smith, I., Zambrana-Torrelio, C., Tao, Y., Islam, A., Quan, P.L., Olival, K.J., Khan, M.S.U., Gurley, E.S., Hossein, M.J., Field, H.E., Fielder, M.D., Briese, T., Rahman, M., Broder, C.C., Crameri, G., Wang, L.-F., Luby, S.P., Lipkin, W.I. & Daszak, P. (2020) Nipah virus dynamics in bats and implications for spillover to humans. Proceedings of the National Academy of Sciences , 202000429.
Ferrari, M.J., Perkins, S.E., Pomeroy, L.W. & Bjørnstad, O.N. (2011) Pathogens, social networks, and the paradox of transmission scaling.Interdisciplinary perspectives on infectious diseases,2011 .
Field, H., Young, P., Yob, J.M., Mills, J., Hall, L. & Mackenzie, J. (2001) The natural history of Hendra and Nipah viruses. Microbes and infection, 3, 307-314.
George, D.B., Webb, C.T., Farnsworth, M.L., O’Shea, T.J., Bowen, R.A., Smith, D.L., Stanley, T.R., Ellison, L.E. & Rupprecht, C.E. (2011) Host and viral ecology determine bat rabies seasonality and maintenance.Proceedings of the National Academy of Sciences, 108,10208-10213.
Giles, J.R., Plowright, R.K., Eby, P., Peel, A.J. & McCallum, H. (2016) Models of Eucalypt phenology predict bat population flux. Ecology and Evolution, 6, 7230-7245.
Goldspink, L.K., Edson, D.W., Vidgen, M.E., Bingham, J., Field, H.E. & Smith, C.S. (2015) Natural Hendra virus infection in flying-foxes-tissue tropism and risk factors. PLoS ONE, 10, e0128835.
Halpin, K., Young, P., Field, H. & Mackenzie, J. (2000) Isolation of Hendra virus from pteropid bats: a natural reservoir of Hendra virus.Journal of General Virology, 81, 1927-1932.
Hayman, D.T. (2015) Biannual birth pulses allow filoviruses to persist in bat populations. Proceedings of the Royal Society B: Biological Sciences, 282, 20142591.
Hopkins, S.R., Fleming‐Davies, A.E., Belden, L.K. & Wojdak, J.M. (2020) Systematic review of modeling assumptions and empirical evidence: does parasite transmission increase nonlinearly with host density?Methods in Ecology and Evolution, 00, 1-11.
Jeong, J., Smith, C., Peel, A.J., Plowright, R.K., Kerlin, D., McBroom, J. & McCallum, H. (2017) Persistent infections support maintenance of a coronavirus in a population of Australian bats (Myotis macropus ).Epidemiology and Infection, 145, 2053-2061.
Jong, M., Diekmann, O. & Heesterbeek, H. (1995) How does transmission of infection depend on population size? Epidemic models.Publication of the Newton Institute , 84-94.
Kerth, G. (2008) Causes and consequences of sociality in bats.Bioscience, 58, 737-746.
Klose, S.M., Welbergen, J.A., Goldizen, A.W. & Kalko, E.K. (2009) Spatio-temporal vigilance architecture of an Australian flying-fox colony. Behavioral Ecology and Sociobiology, 63,371-380.
Krebs, C.J. (1999) Ecological Methodology . Educational Publishers, Inc.
Laurinec, P. (2017) Doing magic and analyzing seasonal time series with GAM (Generalized Additive Model) in R. Time series data mining in R . Bratislava, Slovakia.
Lewis, S.E. (1995) Roost fidelity of bats: a review. Journal of Mammalogy, 76, 481-496.
Lloyd-Smith, J.O., Cross, P.C., Briggs, C.J., Daugherty, M., Getz, W.M., Latto, J., Sanchez, M.S., Smith, A.B. & Swei, A. (2005) Should we expect population thresholds for wildlife disease? Trends in Ecology and Evolution, 20, 511-519.
Lunn, T., Eby, P., Brooks, R., McCallum, H., Plowright, R., Kessler, M. & Peel, A. (2021) Conventional wisdom on roosting behaviour of Australian flying foxes–a critical review, and evaluation using new data. Authorea Preprints .
Lunn, T.J., Restif, O., Peel, A.J., Munster, V.J., De Wit, E., Sokolow, S., Van Doremalen, N., Hudson, P. & McCallum, H. (2019) Dose–response and transmission: the nexus between reservoir hosts, environment and recipient hosts. Philosophical Transactions of the Royal Society B, 374, 20190016.
Markus, N. (2002) Behaviour of the black flying fox Pteropus alecto : 2. Territoriality and courtship. Acta Chiropterologica,4, 153-166.
Markus, N. & Blackshaw, J.K. (2002) Behaviour of the black flying fox Pteropus alecto: 1. An ethogram of behaviour, and preliminary characterisation of mother-infant interactions. Acta Chiropterologica, 4, 137-152.
McCallum, H., Barlow, N. & Hone, J. (2001) How should pathogen transmission be modelled? Trends in Ecology and Evolution,16, 295-300.
McCallum, H., Fenton, A., Hudson, P.J., Lee, B., Levick, B., Norman, R., Perkins, S.E., Viney, M., Wilson, A.J. & Lello, J. (2017) Breaking beta: deconstructing the parasite transmission function.Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences, 372 .
National Flying-Fox Monitoring Program (2017) National flying-fox monitoring viewer. Monitoring flying-fox populations .
Nelson, J.E. (1965) Behaviour of Australian Pteropodidae (Megacheroptera). Animal Behaviour, 13, 544-557.
Orlofske, S.A., Flaxman, S.M., Joseph, M.B., Fenton, A., Melbourne, B.A. & Johnson, P.T. (2017) Experimental investigation of alternative transmission functions: quantitative evidence for the importance of non‐linear transmission dynamics in host‐parasite systems. Journal of Animal Ecology .
Páez, D., Giles, J., McCallum, H., Field, H., Jordan, D., Peel, A. & Plowright, R. (2017) Conditions affecting the timing and magnitude of Hendra virus shedding across pteropodid bat populations in Australia.Epidemiology and Infection , 1-11.
Plowright, R.K., Eby, P., Hudson, P.J., Smith, I.L., Westcott, D., Bryden, W.L., Middleton, D., Reid, P.A., McFarlane, R.A., Martin, G., Tabor, G.M., Skerratt, L.F., Anderson, D.L., Crameri, G., Quammen, D., Jordan, D., Freeman, P., Wang, L.F., Epstein, J.H., Marsh, G.A., Kung, N.Y. & McCallum, H. (2015) Ecological dynamics of emerging bat virus spillover. Proceedings of the Royal Society B-Biological Sciences, 282, 9.
Plowright, R.K., Foley, P., Field, H.E., Dobson, A.P., Foley, J.E., Eby, P. & Daszak, P. (2011) Urban habituation, ecological connectivity and epidemic dampening: the emergence of Hendra virus from flying foxes (Pteropus spp.). Proceedings of the Royal Society of London B: Biological Sciences, 278, 3703-3712.
Restif, O., Hayman, D.T.S., Pulliam, J.R.C., Plowright, R.K., George, D.B., Luis, A.D., Cunningham, A.A., Bowen, R.A., Fooks, A.R., O’Shea, T.J., Wood, J.L.N. & Webb, C.T. (2012) Model-guided fieldwork: practical guidelines for multidisciplinary research on wildlife ecological and epidemiological dynamics. Ecology Letters .
Rhodes, M. (2007) Roost fidelity and fission–fusion dynamics of white-striped free-tailed bats (Tadarida australis ).Journal of Mammalogy, 88, 1252-1260.
Ryder, J.J., Miller, M.R., White, A., Knell, R.J. & Boots, M. (2007) Host-Parasite Population Dynamics under Combined Frequency- and Density-Dependent Transmission. pp. 2017. Blackwell Publishing.
Ryder, J.J., Webberley, K.M., Boots, M. & Knell, R.J. (2005) Measuring the Transmission Dynamics of a Sexually Transmitted Disease. pp. 15140. National Academy of Sciences.
Serra-Cobo, J., Lopez-Roig, M., Segui, M., Sanchez, L.P., Nadal, J., Borras, M., Lavenir, R. & Bourhy, H. (2013) Ecological factors associated with European bat Lyssavirus seroprevalence in Spanish bats.PLoS ONE, 8 .
Smith, M.J., Telfer, S., Kallio, E.R., Burthe, S., Cook, A.R., Lambin, X. & Begon, M. (2009) Host–pathogen time series data in wildlife support a transmission function between density and frequency dependence. Proceedings of the National Academy of Sciences,106, 7905-7909.
Verma, N.K., Lamb, D.W., Reid, N. & Wilson, B. (2014) An allometric model for estimating DBH of isolated and clustered Eucalyptus trees from measurements of crown projection area. Forest Ecology and Management, 326, 125-132.
Veterinary Practitioners Board of New South Wales (2021) NSW DPI Update: Variant Hendra virus strain. (ed. S. Britton). New South Wales.
Wang, H.-H., Kung, N.Y., Grant, W.E., Scanlan, J.C. & Field, H.E. (2013) Recrudescent infection supports Hendra virus persistence in Australian flying-fox populations. PLoS ONE, 8, 1-11.
Welbergen, J.A. (2005) The social organisation of the grey-headed flying-fox, Pteropus poliocephalus . Doctor of Philosophy, University of Cambridge.
Welbergen, J.A., Meade, J., Field, H.E., Edson, D., McMichael, L., Shoo, L.P., Praszczalek, J., Smith, C. & Martin, J.M. (2020) Extreme mobility of the world’s largest flying mammals creates key challenges for management and conservation. BMC biology, 18, 1-13.
Westcott, D.A., McKeown, A., Murphy, H.T. & Fletcher, C.S. (2011) A monitoring method for the grey-headed flying-fox, Pteropus poliocephalus . CSIRO, Queensland, Australia.
Wood, S.N. (2017) Generalized additive models: an introduction with R . CRC press.
Wood, S.W., Prior, L.D., Stephens, H.C. & Bowman, D.M.J.S. (2015) Macroecology of Australian tall eucalypt forests: baseline data from a continental-scale permanent plot network. PLoS ONE, 10,e0137811.
Yang, L., Qin, G., Zhao, N., Wang, C. & Song, G. (2012) Using a generalized additive model with autoregressive terms to study the effects of daily temperature on mortality. BMC Medical Research Methodology, 12, 165.