Long-term transmission dynamics of tick-borne diseases involving seasonal variation and co-feeding transmission. (English) Zbl 1484.92126

Summary: Co-feeding is a mode of pathogen transmission for a wide range of tick-borne diseases where susceptible ticks can acquire infection from co-feeding with infected ticks on the same hosts. The significance of this transmission pathway is determined by the co-occurrence of ticks at different stages in the same season. Taking this into account, we formulate a system of differential equations with tick population dynamics and pathogen transmission dynamics highly regulated by the seasonal temperature variations. We examine the global dynamics of the model systems, and show that the two important ecological and epidemiological basic reproduction numbers can be used to fully characterize the long-term dynamics, and we link these two important threshold values to efficacy of co-feeding transmission.


92D30 Epidemiology
Full Text: DOI


[1] Daniel, M.; Malý, M.; Danielová, V.; Kříž, B.; Nuttall, P., Abiotic predictors and annual seasonal dynamics of Ixodes ricinus, the major disease vector of Central Europe, Parasit. Vectors, 8, 478 (2015)
[2] Eisen, R. J.; Eisen, L.; Ogden, N. H.; Beard, C. B., Linkages of weather and climate with Ixodes scapularis and Ixodes pacificus (Acari: Ixodidae), enzootic transmission of Borrelia burgdorferi, and Lyme disease in North America, J. Med. Entomol., 53, 2, 250-261 (2016)
[3] Fan, G.; Thieme, H. R.; Zhu, H., Delay differential systems for tick population dynamics, J. Math. Biol., 71, 5, 1017-1048 (2015) · Zbl 1355.92087
[4] Fan, G.; Lou, Y.; Thieme, H. R.; Wu, J., Stability and persistence in ODE models for populations with many stages, Math. Biosci. Eng., 12, 661-686 (2015) · Zbl 1369.92095
[5] Gaff, H.; Gross, L.; Schaefer, E., Results from a mathematical model for human monocytic ehrlichiosis, Clin. Microbiol. Infect., 15, 2, 15-16 (2009)
[6] Gern, L.; Rais, O., Efficient transmission of Borrelia burgdorferi between cofeeding Ixodes ricinus ticks (Acari: Ixodidae), J. Med. Entomol., 1, 33, 189-192 (1996)
[7] Hartemink, N. A.; Randolph, S. E.; Davis, S. A.; Heesterbeek, J. A.P., The basic reproduction number for complex disease systems: Defining R0 for tick-borne infections, Am. Nat., 171, 6, 743-754 (2008)
[8] Heffernan, J. M.; Lou, Y.; Wu, J., Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds, Discrete Contin. Dyn. Syst. Ser. B, 19, 10, 3147-3167 (2014) · Zbl 1308.34108
[9] Hirsch, M. W.; Smith, H. L.; Zhao, X. Q., Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dyn. Differ. Equ., 13, 1, 107-131 (2001) · Zbl 1129.37306
[10] Jennings, R.; Kuang, Y.; Thieme, H. R.; Wu, J.; Wu, X., How ticks keep ticking in the adversity of host immune reactions, J. Math. Biol., 78, 5, 1331-1364 (2019) · Zbl 1415.92205
[11] Kato, T., Perturbation Theory for Linear Operators (2013), Springer Science & Business Media: Springer Science & Business Media, Berlin Heidelberg
[12] Kazimírová, M.; Stibraniova, I., Tick salivary compounds: their role in modulation of host defences and pathogen transmission, Front. Cell. Infect. Microbiol., 3, 43 (2013)
[13] Labuda, M.; Jones, L. D.; Williams, T.; Danielova, V.; Nuttall, P. A., Efficient transmission of tick-borne encephalitis virus between cofeeding ticks, J. Med. Entomol., 30, 1, 295-299 (1993)
[14] Labuda, M.; Kozuch, O.; Zuffová, E.; Elecková, E.; Hails, R. S.; Nuttall, P. A., Tick-borne encephalitis virus transmission between ticks cofeeding on specific immune natural rodent hosts, Virology, 235, 1, 138-143 (1997)
[15] Levin, M. L.; Fish, D., Density-dependent factors regulating feeding success of Ixodes scapularis larvae (Acari: Ixodidae), J. Parasitol., 84, 1, 36-43 (1988)
[16] Lou, Y.; Wu, J.; Wu, X., Impact of biodiversity and seasonality on Lyme-pathogen transmission, Theor. Biol. Med. Model., 11, 1, 50 (2014)
[17] Lou, Y.; Liu, L.; Gao, D., Modeling co-infection of Ixodes tick-borne pathogens, Math. Biosci. Eng., 14, 5-6, 1301-1316 (2017) · Zbl 1365.92125
[18] Maliyoni, M.; Chirove, F.; Gaff, H. D.; Govinder, K. S., A stochastic tick-Borne disease model: Exploring the probability of pathogen persistence, Bull. Math. Biol., 79, 1999-2021 (2017) · Zbl 1372.92107
[19] Nah, K.; Magpantay, F. M.G.; Bede-Fazekas, Å.; Röst, G.; Trájer, A. J.; Wu, X.; Zhang, X.; Wu, J., Assessing systemic and non-systemic transmission risk of tick-borne encephalitis virus in Hungary, PloS one, 14, 6, e0217206 (2019)
[20] Norman, R.; Bowers, R. G.; Begon, M.; Hudson, P. J., Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition, J. Theor. Biol., 200, 1, 111-118 (1999)
[21] Norman, R.; Ross, D.; Laurenson, M. K.; Hudson, P. J., 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), J. Math. Biol., 48, 2, 119-134 (2004) · Zbl 1058.92040
[22] Ogden, N. H.; Bigras-Poulin, M.; O’callaghan, C. J.; Barker, I. K.; Lindsay, L. R.; Maarouf, A.; Smoyer-Tomic, K. E.; Waltner-Toews, D.; Charron, D., A dynamic population model to investigate effects of climate on geographic range and seasonality of the tick Ixodes scapularis, Int. J. Parasitol., 35, 4, 375-389 (2005)
[23] Parola, P.; Raoult, D., Ticks and tickborne bacterial diseases in humans: an emerging infectious threat, Clin. Infect. Dis., 32, 6, 897-928 (2001)
[24] Pettersson, J. H.; Golovljova, I.; Vene, S.; Jaenson, T. G., Prevalence of tick-borne encephalitis virus in Ixodes ricinus ticks in northern Europe with particular reference to Southern Sweden, Parasit. Vectors, 7, 1, 102 (2014)
[25] Randolph, S. E., Abiotic and biotic determinants of the seasonal dynamics of the tick Rhipicephalus appendiculatus in South Africa, Med. Vet. Entomol., 11, 1, 25-37 (1997)
[26] Randolph, S. E., Transmission of tick-borne pathogens between co-feeding ticks: Milan Labuda’s enduring paradigm, Ticks Tick-Borne Dis., 2, 4, 179-182 (2011)
[27] Randolph, S. E.; Gern, L.; Nuttall, P. A., Co-feeding ticks: epidemiological significance for tick-borne pathogen transmission, Parasitol. Today, 12, 12, 472-479 (1996)
[28] Randolph, S. E.; Miklisova, D.; Lysy, J.; Rogers, D. J.; Labuda, M., Incidence from coincidence: patterns of tick infestations on rodents facilitate transmission of tick-borne encephalitis virus, Parasitol., 118, 2, 177-186 (1999)
[29] Richter, D.; Allgöwer, R.; Matuschka, F. R., Co-feeding transmission and its contribution to the perpetuation of the Lyme disease spirochete Borrelia afzelii, Emerg. Infect. Dis., 8, 12, 1421-1425 (2002)
[30] Rosà, R.; Pugliese, A., Effects of tick population dynamics and host densities on the persistence of tick-borne infections, Math. Biosci.,, 208, 1, 216-240 (2007) · Zbl 1116.92057
[31] Rosà, R.; Pugliese, A.; Norman, R.; Hudson, P. J., Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation, J. Theor. Biol., 224, 3, 359-376 (2003) · Zbl 1465.92128
[32] Smith, H. L., Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Amer. Math. Soc., 41, 81-84 (1995) · Zbl 0821.34003
[33] Van den Driessche, P.; Watmough, J., Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180, 1-2, 29-48 (2002) · Zbl 1015.92036
[34] Voordouw, M. J., Co-feeding transmission in Lyme disease pathogens, Parasitology, 142, 2, 290-302 (2015)
[35] Wang, W.; Zhao, X. Q., Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Equ., 20, 3, 699-717 (2008) · Zbl 1157.34041
[36] White, A.; Schaefer, E.; Thompson, C. W.; Kribs, C. M.; Gaff, H., Dynamics of two pathogens in a single tick population, Lett. Biomath., 6, 1, 50-66 (2019)
[37] Wu, X.; Wu, J., Diffusive systems with seasonality: eventually strongly order-preserving periodic processes and range expansion of tick populations, Canad. Appl. Math. Quart., 20, 557-587 (2012) · Zbl 1322.92065
[38] Wu, J.; Zhang, X., Transmission Dynamics of Tick-Borne Diseases with Co-Feeding, Developmental and Behavioural Diapause (2020), Springer Nature: Springer Nature, Switzerland AG · Zbl 1451.92003
[39] Zhang, X.; Wu, J., Implications of vector attachment and host grooming behaviour for vector population dynamics and distribution of vectors on their hosts, Appl. Math. Model., 81, 1-15 (2020) · Zbl 1481.92126
[40] Zhang, X.; Wu, X.; Wu, J., Critical contact rate for vector-host-pathogen oscillation involving co-feeding and diapause, J. Biol. Syst., 25, 4, 657-675 (2017) · Zbl 1397.92702
[41] Zhao, X. Q., Dynamical Systems in Population Biology (2003), Springer: Springer, New York · Zbl 1023.37047
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