Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-23T05:47:11.912Z Has data issue: false hasContentIssue false

Past and future perspectives on mathematical models of tick-borne pathogens

Published online by Cambridge University Press:  18 December 2015

R. A. NORMAN*
Affiliation:
School of Natural Sciences, University of Stirling, Stirling FK9 4LA, UK
A. J. WORTON
Affiliation:
Division of Computing Science and Mathematics, University of Stirling, Stirling FK9 4LA, UK
L. GILBERT
Affiliation:
The James Hutton Institute, Craigiebuckler, Aberdeen AB15 8QH, UK
*
*Corresponding author. School of Natural Sciences, University of Stirling, Stirling FK9 4LA, UK. E-mail: r.a.norman@stir.ac.uk

Summary

Ticks are vectors of pathogens which are important both with respect to human health and economically. They have a complex life cycle requiring several blood meals throughout their life. These blood meals take place on different individual hosts and potentially on different host species. Their life cycle is also dependent on environmental conditions such as the temperature and habitat type. Mathematical models have been used for the more than 30 years to help us understand how tick dynamics are dependent on these environmental factors and host availability. In this paper, we review models of tick dynamics and summarize the main results. This summary is split into two parts, one which looks at tick dynamics and one which looks at tick-borne pathogens. In general, the models of tick dynamics are used to determine when the peak in tick densities is likely to occur in the year and how that changes with environmental conditions. The models of tick-borne pathogens focus more on the conditions under which the pathogen can persist and how host population densities might be manipulated to control these pathogens. In the final section of the paper, we identify gaps in the current knowledge and future modelling approaches. These include spatial models linked to environmental information and Geographic Information System maps, and development of new modelling techniques which model tick densities per host more explicitly.

Type
Special Issue Article
Copyright
Copyright © Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bolzoni, L., Rosa, R., Cagnacci, F. and Rizzoli, A. (2012). Effect of deer density on tick infestation of rodents and the hazard of tick-borne encephalitis. II: population and infection models. International Journal for Parasitology 42, 373381.Google Scholar
Braga, J. F. (2012). Predicting current and future tick abundance across Scotland . Masters thesis, University of Aberdeen, UK.Google Scholar
Cagnacci, F., Bolzoni, L., Rosa, R., Carpi, G., Hauffe, H. C., Valent, M., Tagliapietra, V., Kazimirova, M., Koci, J., Stanko, M., Lukan, M., Henttonen, H. and Rizzoli, A. (2012). Effects of deer density on tick infestation of rodents and the hazard of tick-borne encephalitis. I: empirical assessment. International Journal of Parasitology 42, 365372.CrossRefGoogle ScholarPubMed
Cooksey, L. M., Haile, D. G. and Mount, G. A. (1990). Computer simulation of rocky mountain spotted fever transmission by the American dog tick (Acari, Ixodidae). Journal of Medical Entomology 27, 686696.CrossRefGoogle ScholarPubMed
Diekmann, O., Heesterbeek, J. A. P. and Roberts, M. G. (2010). The construction of next-generation matrices for compartmental epidemic models. Journal of the Royal Society Interface 7, 873885.Google Scholar
Dobson, A. (2014). History and complexity in tick-host dynamics: discrepancies between ‘real’ and ‘visible’ tick populations. Parasites and Vectors 7, 231.CrossRefGoogle ScholarPubMed
Dobson, A. and Randolph, S. (2011 a). Modelling the effects of recent changes in climate, host density and acaricide treatments on population dynamics of Ixodes ricinus in the UK. Journal of Applied Ecology 48, 10291037.Google Scholar
Dobson, A., Finnie, T. and Randolph, S. (2011 b). A modified matrix model to describe the seasonal population ecology of the European tick Ixodes ricinus . Journal of Applied Ecology 48, 10171028.CrossRefGoogle Scholar
Dunn, J. M., Davis, S., Staecy, A. and Diuk-Wasser, M. A. (2013). A simple model for the establishment of tick-borne pathogens of Ixodes scapularis: a global sensitivity analysis of R0 . Journal of Theoretical Biology 335, 213221.Google Scholar
Ferreri, L., Giacobini, M., bajardi, P., Bertolotti, L., Bolzoni, L., Tagliapietre, V., Rizzoli, A. and Rosa, R. (2014). Pattern of tick aggregation on mice: larger than expected distribution tail enhances the spread of tick-borne pathogens. PLoS Computational Biology 10, e1003931.Google Scholar
Gardiner, W. P., Gettinby, G. and Gray, J. S. (1981). Models based on weather for the development phases of the sheep tick, Ixodes ricinus L. Veterinary Parasitology 9, 7586.Google Scholar
Gilbert, L. (2015). Louping ill virus in the UK: a review of the hosts, transmission and ecological consequences of control. Experimental and Applied Acarology pp. 112. DOI 10.1007/s10493-015-9952-xFirst online: 24 July 2015.Google Scholar
Gilbert, L., Aungier, J. and Tomkins, J. L. (2014). Climate of origin affects tick (Ixodes ricinus) host-seeking behaviour in response to temperature: implications for resilience to climate change? Ecology and Evolution 4, 11861198.CrossRefGoogle ScholarPubMed
Gilbert, L., Norman, R., Laurenson, K. M., Reid, H. W. and Hudson, P. J. (2001). Disease persistence and apparent competition in a three-host community: an empirical and analytical study of large-scale, wild populations. Journal of Animal Ecology 70, 10531061.Google Scholar
Gilbert, L., Jones, L. D., Laurenson, M. K., Gould, E. A., Reid, H. W. and Hudson, P. J. (2004). Ticks need not bite their red grouse hosts to infect them with louping ill virus. Proceedings of the Royal Society B, Biological Sciences 271, S202S205.Google Scholar
Gilbert, L., Maffey, G., Ramsay, S. L. and Hester, A. J. (2012). The effect of deer management on the abundance of Ixodes ricinus in Scotland. Ecological Applications 22, 658667.Google Scholar
Gray, J. S. (1987). Mating and behavioural diapause in Ixodes ricinus L. Experimental and Applied Acarology 3, 6171.Google Scholar
Gray, J. S. (1998). The ecology of ticks transmitting Lyme borreliosis . Experimental and Applied Acarology. 22, 249258.Google Scholar
Hancock, P., Brackley, R. and Palmer, S. (2011). Modelling the effect of temperature variation on the seasonal dynamics of Ixodes ricinus tick populations. International Journal for Parasitology 41, 513522.CrossRefGoogle ScholarPubMed
Harrison, A., Newey, S., Gilbert, L., Haydon, D. T. and Thirgood, S. (2010). Culling wildlife hosts to control disease: mountain hares, red grouse and louping ill virus. Journal of Applied Ecology 47, 926930.Google Scholar
Hartemink, N. A., Randolph, S. E., Davis, S. A. and Heesterbeek, J. A. P. (2008). The basic reproduction number for complex disease systems: defining R-0 for tick-borne infections. American Naturalist 171, 743754.Google Scholar
Hönig, V., Švec, P., Masař, O. and Grubhoffer, L. (2011). Tick-borne disease risk model for South Bohemia (Czech Republic). In GIS Ostrava 2011, Proceedings of Eighth International Symposium, ISBN 978-80-248-2406-2. 255268.Google Scholar
Hudson, P. J., Norman, R., Laurenson, M. K., Newborn, D., Gaunt, M., Gould, E., Reid, H., Bowers, R. G. and Dobson, A. P. (1995). Persistence and transmission of tick-borne viruses: Ixodes ricinus and louping Ill virus in red grouse populations. Parasitology 111, s49s58.Google Scholar
Jones, L. D., Davies, C. R., Steele, C. M. and Nuttall, P. A. (1987). A novel mode of arbovirus transmission involving a nonviraemic host. Science 237, 775777.Google Scholar
Jones, L. D., Gaunt, M., Hails, R. S., Laurenson, K., Hudson, P. J., Reid, H., Henbest, P. and Gould, E. A. (1997). Efficient transfer of louping-ill virus between infected and uninfected ticks co-feeding on mountain hares (Lepus timidus). Medical and veterinary Entomology 11, 172176.Google Scholar
Jones, E. O., Webb, S. D., Ruiz-Fons, F. J., Albon, S. and Gilbert, L. (2011). The effect of landscape heterogeneity and host movement on a tick-borne pathogen. Theoretical Ecology 4, 435448.CrossRefGoogle Scholar
Jore, S., Viljugrein, H., Hofshagen, M., Brun-Hansen, H., Kristoffersen, A. B., Nygård, K., Brun, E., Ottesen, P., Sævik, B. K. and Ytrehus, B. (2011). Multi-source analysis reveals latitudinal and altitudinal shifts in range of Ixodes ricinus at its northern distribution limit. Parasites & Vectors 4. Article Number 84.Google Scholar
Labuda, M. and Nuttall, P. A. (2004). Tick borne viruses. Parasitology. 129, S221S245.Google Scholar
Laurenson, M. K., Norman, R., Reid, H. W., Pow, I., Newborn, D. and Hudson, P. J. (2000). The role of lambs in louping-ill virus amplification. Parasitology 120, 97104.CrossRefGoogle ScholarPubMed
Laurenson, M. K., Norman, R. A., Gilbert, L., Reid, H. W. and Hudson, P. J. (2003). Identifying disease reservoirs in complex systems: mountain hares as reservoirs of ticks and louping-ill virus, pathogens of red grouse. Journal of Animal Ecology 72, 177185.Google Scholar
Lorenz, A., Dhingra, R., Chang, H. H., Bisanzio, D., Liu, Y. and Remais, J. V. (2014). Inter-model comparison of the landscape determinants of vector-borne disease: implications for epidemiological and entomological risk modeling. PLoS ONE 9, e103163.Google Scholar
Medlock, J., Hansford, K. M., Bormane, A., Derdakova, M., Estrada-Peña, A., George, J. C., Golovljova, I., Jaenson, T. G., Jensen, J. K., Jensen, P. M., Kazimirova, M., Oteo, J. A., Papa, A., Pfister, K., Plantard, O., Randolph, S. E., Rizzoli, A., Santos-Silva, M. M., Sprong, H., Vial, L., Hendrickx, G., Zeller, H. and Van Bortel, W. (2013). Driving forces for changes in geographical distribution of Ixodes ricinus ticks in Europe. Parasites & Vectors 6, 1.Google Scholar
Mount, G. A. and Haile, D. G. (1989). Computer simulation of population dynamics of the American dog tick (Acari: Ixodidae). Journal of Medical Entomology 26, 6076.Google Scholar
Norman, R., Bowers, R. G., Begon, M. and Hudson, P. J. (1999). Persistence and dynamics of louping Ill in relation to host abundance. Journal of Theoretical Biology 200, 111118.Google Scholar
Norman, R., Ross, D., Laurenson, M. K., and Hudson, P. J. (2004). The role of non-viraemic transmission on the persistence and dynamics of a tick-borne virus louping ill in red grouse (Lagopus lagopus scoticus) and mountain hares (Lepus timidus). Journal of Mathematical Biology 48, 119134.Google Scholar
Nuttall, P. A. and Jones, L. D. (1991). Non-viraemic tick-borne virus transmission: mechanism and significance. In Modern Acarology. Volume II: Proceedings of the Eighth International Congress of Acarology held in Ceske Budejovice, Czechoslovakia (ed. Dusbabek, F., Buvka, V.), pp. 36. Ceske Budejovice, Czechoslovakia, 6–11 August 1990.Google Scholar
Ogden, N. H., Lindsay, A. R., Charron, D., Beauchamp, G., Maarouf, A., O'Callaghan, C. J., Waltner-Tiews, D. and Barker, I. K. (2004). Investigation of the relationships between temperature and development rates of the tick Ixodes scapularis (Acari: Ixodidae) in the laboratory and field. Journal of Medical Entomology, 41, 622633.Google Scholar
Ogden, N. H., Bigras-Poulin, M., O'Callaghan, C. J., Barker, I. K., Lindsay, L. R., Maarouf, A., Smoyer-omic, K. E., Waltner-Toews, D. and Charron, D. (2005). A dynamic population model to investigate effects of climate on geographic range and seasonality of the tick Ixodes scapularis . International Journal for Parasitology 35, 375389.Google Scholar
Ogden, N. H., Bigras-Poulin, M., O'Callaghan, C. J., Barker, I. K., Kurtenbach, K., Lindsay, L. R. and Charron, D. F. (2007). Vector seasonality, host infection dynamics and fitness of pathogens transmitted by the tick Ixodes scapularis . Parasitology 134, 209227.Google Scholar
Ogden, N. H., Lindsay, L. R. and Leighton, P. A. (2013). Predicting the rate of invasion of the agent of Lyme disease Borrelia burgdorferi. Journal of Applied Ecology 50, 510518.Google Scholar
Park, K. J., Robertson, P. A., Campbell, S. T., Foster, R., Russell, Z. M., Newborn, D. and Hudson, P. J. (2001). The role of invertebrates in the diet, growth and survival of red grouse (Lagopus lagopus scoticus) chicks. Journal of Zoology 254, 137145.Google Scholar
Perkins, S. (2003). Transmission dynamics of tick-borne diseases associated with small mammals . Ph.D. thesis, University of Stirling, Scotland, UK.Google Scholar
Perret, J. L., Guigoz, E., Rais, O. and Gern, L. (2000). Influence of saturation deficit and temperature on Ixodes ricinus tick questing activity in a Lyme borreliosis-endemic area (Switzerland). Parasitology Research 86, 554557.Google Scholar
Porco, T. C. (1999). A mathematical model of the ecology of Lyme disease. IMA Journal of Mathematics Applied in Medicine and Biology 16, 261296.Google Scholar
Porter, R., Norman, R. and Gilbert, L. (2011). Controlling tick-borne diseases through domestic animal management: a theoretical approach. Theoretical Ecology 4, 321339.CrossRefGoogle Scholar
Porter, R., Norman, R. A. and Gilbert, L. (2013 a). An alternative to killing? Treating wildlife hosts to protect a valuable species from a shared parasite. Parasitology 140, 247–225.Google Scholar
Porter, R., Norman, R. and Gilbert, L. (2013 b). An empirical model to test how ticks and louping ill virus can be controlled by treating red grouse with acaricide. Medical Veterinary Entomology 27, 237246. 10.Google Scholar
Randolph, S. E. (2008). Dynamics of tick-borne disease systems: minor role of recent climate change. Revue Scientifique et Technique, Office International des Epizooties 27, 367–281.Google Scholar
Randolph, S. E. and Rogers, D. J. (1997). A generic population model for the African tick Rhipicephalus appendiculatus . Parasitology 115, 265279.CrossRefGoogle ScholarPubMed
Randolph, S. E., Green, R., Hoodless, A. and Peacey, M. F. (2002). An empirical, quantitative framework for the seasonal population dynamics of the tick Ixodes ricinus . International Journal for Parasitology 32, 979989.Google Scholar
Reid, H. W. (1976). The epidemiology of Louping-ill. In: Tick-Borne Diseases and Their Vectors (ed. Wilde, J. K. H.), Proceedings of the International Conference held in Edinburgh September 27 October 1, 1976. Edinburgh University Press, UK.Google Scholar
Rosa, R. and Pugliese, A. (2007). Effects of tick population dynamics and host densities on the persistence of tick-borne infections. Mathematical Biosciences 208, 216240.Google Scholar
Rosa, R., Pugliese, A., Norman, R. and Hudson, P. J. (2003). Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation. Journal of Theoretical Biology 224, 359376.Google Scholar
Ruiz-Fons, F. and Gilbert, L. (2010). The role of deer (Cervus elaphus and Capreolus capreolus) as vehicles to move ticks Ixodes ricinus between contrasting habitats. International Journal for Parasitology 40, 10131020.CrossRefGoogle Scholar
Schwarz, A., Maier, W. A., Kistemann, T., Kampen, H. (2009). Analysis of the distribution of the tick Ixodes ricinus L. (Acari: Ixodidae) in a nature reserve of western Germany using geographic information systems. International Journal of Hygiene and Environmental Health 212, 8796.CrossRefGoogle Scholar
Tagliapietra, V., Rosa, R., Arnoldi, D., Cagnacci, F., Capelli, G., Montarsi, F., Hauffe, H. C. and Rizzoli, A. (2011). Saturation deficit and deer density affect questing activity and local abundance of Ixodes ricinus (Acari, Ixodidae) in Italy. Veterinary Parasitology 183, 114124.Google Scholar
Tomkins, J. L., Aungier, J., Hazel, W. and Gilbert, L. (2014). Towards an evolutionary understanding of host seeking behaviour in the Borrelia burgdorferi sensu lato vector Ixodes ricinus: data and theory. PLoS ONE 9, e110028.Google Scholar
Watts, E. J., Palmer, S. C. F., Bowman, A. S., Irvine, R. J., Smith, A. and Travis, J. M. J. (2009). The effect of host movement on viral transmission dynamics in a vector-borne disease system. Parasitology 136, 12211234.Google Scholar
Wilson, M. L. and Spielman, A. (1985). Seasonal activity of immature Ixodes dammini (Acari:Ixodidae). Journal of Medical Entomology 26, 408414.Google Scholar
Wu, X., Duvvuri, V. R., Lou, Y., Ogden, N. H., Pelcat, Y. and Wu, J. (2013). Developing a temperature-driven map of the basic reproductive number of the emerging tick vector of Lyme disease Ixodes scapularis in Canada. Journal of Theoretical Biology 319, 5061.Google Scholar
Zeman, P. (1997). Objective assessment of risk maps of tick-born encephalitis and Lyme Borreliosis based on spatial patterns of located cases. International Journal of Epidemiology 26, 11211130.Google Scholar
Zeman, P., Pazdiora, P. and Benes, C. (2010). Spatio-temporal variation of tick-borne encephalitis (TBE) incidence in the Czech Republic: is the current explanation of the disease's rise satisfactory? Ticks and Tick-borne Diseases 1, 129140.Google Scholar
Zhang, Y. and Zhao, X.-Q. (2013). A reaction-diffusion Lyme disease model with seasonality. Society for Industrial and Applied Mathematics 73, 20772099.Google Scholar