Long-term transmission dynamics of tick-borne diseases involving seasonal variation and co-feeding transmission

References

• M. Daniel, M. Malý, V. Danielová, B. Kříž, and P. Nuttall, Abiotic predictors and annual seasonal dynamics of Ixodes ricinus, the major disease vector of Central Europe, Parasit. Vectors 8 (2015), p. 478.
   PubMed Web of Science ®Google Scholar
• R.J. Eisen, L. Eisen, N.H. Ogden, and C.B. Beard, 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) (2016), pp. 250–261.
   PubMed Web of Science ®Google Scholar
• G. Fan, H.R. Thieme, and H. Zhu, Delay differential systems for tick population dynamics, J. Math. Biol. 71(5) (2015), pp. 1017–1048.
   PubMed Web of Science ®Google Scholar
• G. Fan, Y. Lou, H.R. Thieme, and J. Wu, Stability and persistence in ODE models for populations with many stages, Math. Biosci. Eng. 12 (2015), pp. 661–686.
   PubMed Web of Science ®Google Scholar
• H. Gaff, L. Gross, and E. Schaefer, Results from a mathematical model for human monocytic ehrlichiosis, Clin. Microbiol. Infect. 15(2) (2009), pp. 15–16.
   PubMedGoogle Scholar
• L. Gern and O. Rais, Efficient transmission of Borrelia burgdorferi between cofeeding Ixodes ricinus ticks (Acari: Ixodidae), J. Med. Entomol. 1(33) (1996), pp. 189–192.
   Google Scholar
• N.A. Hartemink, S.E. Randolph, S.A. Davis, and J.A.P. Heesterbeek, The basic reproduction number for complex disease systems: Defining R0 for tick-borne infections, Am. Nat. 171(6) (2008), pp. 743–754.
   PubMed Web of Science ®Google Scholar
• J.M. Heffernan, Y. Lou, and J. Wu, Range expansion of Ixodes scapularis ticks and of Borrelia burgdorferi by migratory birds, Discrete Contin. Dyn. Syst. Ser. B 19(10) (2014), pp. 3147–3167.
   Web of Science ®Google Scholar
• M.W. Hirsch, H.L. Smith, and X.Q. Zhao, Chain transitivity, attractivity, and strong repellors for semidynamical systems, J. Dyn. Differ. Equ. 13(1) (2001), pp. 107–131.
   Google Scholar
• R. Jennings, Y. Kuang, H.R. Thieme, J. Wu, and X. Wu, How ticks keep ticking in the adversity of host immune reactions, J. Math. Biol. 78(5) (2019), pp. 1331–1364.
   PubMed Web of Science ®Google Scholar
• T. Kato, Perturbation Theory for Linear Operators, Springer Science & Business Media, Berlin Heidelberg, 2013.
   Google Scholar
• M. Kazimírová and I. Stibraniova, Tick salivary compounds: their role in modulation of host defences and pathogen transmission, Front. Cell. Infect. Microbiol. 3 (2013), p. 43.
   PubMed Web of Science ®Google Scholar
• M. Labuda, L.D. Jones, T. Williams, V. Danielova, and P.A. Nuttall, Efficient transmission of tick-borne encephalitis virus between cofeeding ticks, J. Med. Entomol. 30(1) (1993), pp. 295–299.
   PubMed Web of Science ®Google Scholar
• M. Labuda, O. Kozuch, E. Zuffová, E. Elecková, R.S. Hails, and P.A. Nuttall, Tick-borne encephalitis virus transmission between ticks cofeeding on specific immune natural rodent hosts, Virology 235(1) (1997), pp. 138–143.
   PubMed Web of Science ®Google Scholar
• M.L. Levin, D. Fish, Density-dependent factors regulating feeding success of Ixodes scapularis larvae (Acari: Ixodidae), J. Parasitol. 84(1) (1988), pp. 36–43.
   Google Scholar
• Y. Lou, J. Wu, and X. Wu, Impact of biodiversity and seasonality on Lyme-pathogen transmission, Theor. Biol. Med. Model. 11(1) (2014), p. 50.
   PubMedGoogle Scholar
• Y. Lou, L. Liu, and D. Gao, Modeling co-infection of Ixodes tick-borne pathogens, Math. Biosci. Eng.14(5&6) (2017), pp. 1301–1316.
   PubMed Web of Science ®Google Scholar
• M. Maliyoni, F. Chirove, H.D. Gaff, and K.S. Govinder, A stochastic tick-Borne disease model: Exploring the probability of pathogen persistence, Bull. Math. Biol. 79 (2017), 1999–2021.
   PubMed Web of Science ®Google Scholar
• K. Nah, F.M.G. Magpantay, Å. Bede-Fazekas, G. Röst, A.J. Trájer, X. Wu, X. Zhang, and J. Wu, Assessing systemic and non-systemic transmission risk of tick-borne encephalitis virus in Hungary, PloS one 14(6) (2019), p. e0217206.
   PubMed Web of Science ®Google Scholar
• R. Norman, R.G. Bowers, M. Begon, and P.J. Hudson, Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition, J. Theor. Biol. 200(1) (1999), pp. 111–118.
   PubMed Web of Science ®Google Scholar
• R. Norman, D. Ross, M.K. Laurenson, and P.J. Hudson, 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) (2004), pp. 119–134.
   PubMed Web of Science ®Google Scholar
• N.H. Ogden, M. Bigras-Poulin, C.J. O'callaghan, I.K. Barker, L.R. Lindsay, A. Maarouf, K.E.Smoyer-Tomic, D. Waltner-Toews, and D. Charron, A dynamic population model to investigate effects of climate on geographic range and seasonality of the tick Ixodes scapularis, Int. J. Parasitol. 35(4) (2005), pp. 375–389.
   PubMed Web of Science ®Google Scholar
• P. Parola and D. Raoult, Ticks and tickborne bacterial diseases in humans: an emerging infectious threat, Clin. Infect. Dis. 32(6) (2001), pp. 897–928.
   PubMed Web of Science ®Google Scholar
• J.H. Pettersson, I. Golovljova, S. Vene, and T.G. Jaenson, Prevalence of tick-borne encephalitis virus in Ixodes ricinus ticks in northern Europe with particular reference to Southern Sweden, Parasit. Vectors7(1) (2014), p. 102.
   PubMedGoogle Scholar
• S.E. Randolph, Abiotic and biotic determinants of the seasonal dynamics of the tick Rhipicephalus appendiculatus in South Africa, Med. Vet. Entomol. 11(1) (1997), pp. 25–37.
   PubMed Web of Science ®Google Scholar
• S.E. Randolph, Transmission of tick-borne pathogens between co-feeding ticks: Milan Labuda's enduring paradigm, Ticks Tick-Borne Dis. 2(4) (2011), pp. 179–182.
   PubMed Web of Science ®Google Scholar
• S.E. Randolph, L. Gern, and P.A. Nuttall, Co-feeding ticks: epidemiological significance for tick-borne pathogen transmission, Parasitol. Today 12(12) (1996), pp. 472–479.
   PubMedGoogle Scholar
• S.E. Randolph, D. Miklisova, J. Lysy, D.J. Rogers, and M. Labuda, Incidence from coincidence: patterns of tick infestations on rodents facilitate transmission of tick-borne encephalitis virus, Parasitol.118(2) (1999), pp. 177–186.
   PubMed Web of Science ®Google Scholar
• D. Richter, R. Allgöwer, and F.R. Matuschka, Co-feeding transmission and its contribution to the perpetuation of the Lyme disease spirochete Borrelia afzelii, Emerg. Infect. Dis. 8(12) (2002), pp. 1421–1425.
   PubMed Web of Science ®Google Scholar
• R. Rosà and A. Pugliese, Effects of tick population dynamics and host densities on the persistence of tick-borne infections, Math. Biosci., 208(1) (2007), pp. 216–240.
   PubMed Web of Science ®Google Scholar
• R. Rosà, A. Pugliese, R. Norman, and P.J. Hudson, Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation, J. Theor. Biol. 224(3) (2003), pp. 359–376.
   PubMed Web of Science ®Google Scholar
• H.L. Smith, Monotone dynamical systems: an introduction to the theory of competitive and cooperative systems, Amer. Math. Soc. 41 (1995), pp. 81–84.
   Google Scholar
• P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci. 180(1–2) (2002), pp. 29–48.
   PubMed Web of Science ®Google Scholar
• M.J. Voordouw, Co-feeding transmission in Lyme disease pathogens, Parasitology 142(2) (2015), pp. 290–302.
   PubMed Web of Science ®Google Scholar
• W. Wang and X.Q. Zhao, Threshold dynamics for compartmental epidemic models in periodic environments, J. Dyn. Differ. Equ. 20(3) (2008), pp. 699–717.
   Web of Science ®Google Scholar
• A. White, E. Schaefer, C.W. Thompson, C.M. Kribs, and H. Gaff, Dynamics of two pathogens in a single tick population, Lett. Biomath. 6(1) (2019), pp. 50–66.
   PubMedGoogle Scholar
• X. Wu and J. Wu, Diffusive systems with seasonality: eventually strongly order-preserving periodic processes and range expansion of tick populations, Canad. Appl. Math. Quart. 20 (2012), pp. 557–587.
   Google Scholar
• J. Wu, X. Zhang, Transmission Dynamics of Tick-Borne Diseases with Co-Feeding, Developmental and Behavioural Diapause, Springer Nature, Switzerland AG, 2020.
   Google Scholar
• X. Zhang and J. Wu, Implications of vector attachment and host grooming behaviour for vector population dynamics and distribution of vectors on their hosts, Appl. Math. Model. 81 (2020), pp. 1–15.
   Web of Science ®Google Scholar
• X. Zhang, X. Wu, and J. Wu, Critical contact rate for vector-host-pathogen oscillation involving co-feeding and diapause, J. Biol. Syst. 25(04) (2017), pp. 657–675.
   Google Scholar
• X.Q. Zhao, Dynamical Systems in Population Biology, Springer, New York, 2003.
   Google Scholar