×

Thresholds for disease persistence in models for tick-borne infections including non-viraemic transmission, extended feeding and tick aggregation. (English) Zbl 1465.92128

This paper studies thresholds for disease persistence is models for tick-borne infections. In the model, ticks are categorized as per their stage as larvae, nymphs and adults. Each larvae and nymphs stage requires a blood meal from a vertebrate host. The model has two classes of hosts: viraemic hosts and non-viraemic hosts. The work considers the possibility of non-viraemic transmission which is relevant to infections such as tick-borne encephalitis. The distribution of tick stages among hosts are studied. Both immature tick stages show highly aggregated distribution on their host and these aggregated distributions are coincident rather than independent. Basic reproduction numbers in several cases have been derived. Together with stability analysis of disease-free equilibrium with only viraemic transmission, stability of disease-free equilibrium with non-viraemic transmission has also been investigated. Some numerical results have been produced to illustrate the theoretical results.

MSC:

92D30 Epidemiology
34D20 Stability of solutions to ordinary differential equations
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Anderson, R.M., May, R.M., 1978. Regulation and stability of host-parasite populations interactions I-II. J. Anim. Ecol. 47, 219-247, 249-267.; Anderson, R.M., May, R.M., 1978. Regulation and stability of host-parasite populations interactions I-II. J. Anim. Ecol. 47, 219-247, 249-267.
[2] Caraco, T., Gardner, G., Szymanski, B.K., 1998. Lyme disease: self-regulation and pathogen invasion. J. Theor. Biol. 193, 561-575, doi:10.1006/jtbi.1998.0722.; Caraco, T., Gardner, G., Szymanski, B.K., 1998. Lyme disease: self-regulation and pathogen invasion. J. Theor. Biol. 193, 561-575, doi:10.1006/jtbi.1998.0722.
[3] Diekmann, O.; Heesterbeek, J. A.P., Mathematical Epidemiology of Infectious Diseases (2000), Wiley: Wiley New York, USA · Zbl 0997.92505
[4] Gilbert, L.; Norman, R.; Laurenson, K. M.; Reid, H. W.; Hudson, P. J., Disease persistence and apparent competition in a three-host communityan empirical and analytical study of large-scale, wild populations, J. Anim. Ecol., 70, 1053-1061 (2001)
[5] Hudson, P. J.; Norman, R.; Laurenson, M. K.; Newborn, D.; Gaunt, M.; Jones, L.; Reid, H.; Gould, E.; Bowers, R.; Dobson, A. P., Persistence and transmission of tick-borne virusesIxodes ricinus and louping-ill virus in red grouse populations, Parasitology, 111, S49-S58 (1995)
[6] Hudson, P. J.; Rizzoli, A.; Grenfell, B. T.; Heesterbeek, H.; Dobson, A. P., Ecology of Wildlife Diseases (2002), Oxford University Press: Oxford University Press Oxford
[7] Humair, P. F.; Rais, O.; Gern, L., Transmission of Borrelia afzelii from Apodemus mice and Clethrionomys voles to Ixodes ricinus ticksdifferential transmission pattern and overwintering maintenance, Parasitology, 118, 33-42 (1999)
[8] Jones, L. D.; Davies, C. R.; Steele, G. M.; Nuttall, P. A., A novel mode of arbovirus transmission involving a nonviraemic host, Science, 37, 775-777 (1987)
[9] Kitron, U.; Mannelli, A., Modeling the ecological dynamics of tick-borne zoonoses, (Mather, T. N.; Sonenshine, D. E., Ecological Dynamics of Tick-Borne Zoonoses (1994), Oxford University Press: Oxford University Press Oxford), 198-239
[10] Labuda, M.; Jones, L. D.; Williams, T.; Danielova, V.; Nuttall, P. A., Efficient transmission of tick-borne encephalitis virus between co-feeding ticks, J. Med. Entom., 30, 295-299 (1993)
[11] Mannelli, A. Effetto della composizione delle popolazioni faunistiche sulla trasmissione di Borrelia burgdorferi s.l. da parte di Ixodes ricinus: studio con un modello di simulazione. Proceedings of the II National Conference of the Italian Wildlife Diseases Association, Bormio (SO), Italy, October 1998. Suppl. Ric. Biol. Selv. (in press).; Mannelli, A. Effetto della composizione delle popolazioni faunistiche sulla trasmissione di Borrelia burgdorferi s.l. da parte di Ixodes ricinus: studio con un modello di simulazione. Proceedings of the II National Conference of the Italian Wildlife Diseases Association, Bormio (SO), Italy, October 1998. Suppl. Ric. Biol. Selv. (in press).
[12] Mwambi, H. G.; Baumgartner, J.; Hadeler, K. P., Ticks and tick-borne diseasesa vector-host interaction model for the brown ear tick, Stat. Meth. Med. Res., 9, 279-301 (2000) · Zbl 1121.62643
[13] Norman, R., Bowers, R.G., Begon, M., Hudson, P.J., 1999. Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition. J. Theor. Biol. 200, 111-118, doi:10.1006/jtbi.1999.0982.; Norman, R., Bowers, R.G., Begon, M., Hudson, P.J., 1999. Persistence of tick-borne virus in the presence of multiple host species: tick reservoirs and parasite mediated competition. J. Theor. Biol. 200, 111-118, doi:10.1006/jtbi.1999.0982.
[14] O’Callaghan, C. J.; Medley, G. F.; Peter, T. F.; Perry, D. J., Investigating the epidemiology of heartwater by means of a transmission dynamics model, Parasitology, 115, 265-279 (1997)
[15] Ogden, N. H.; Nuttall, P. A.; Randolph, S. E., Natural Lyme disease cycles maintained via sheep by cofeeding ticks, Parasitology, 115, 591-599 (1997)
[16] Puccia, C. J.; Levins, R., Qualitative Modeling of Complex Systems (1985), Harvard University Press: Harvard University Press Cambridge, Massachusetts, London, England
[17] Randolph, S. E.; Rogers, D. J., A generic population model for the African tick Rhipicephalus appendiculatus, Parasitology, 115, 265-279 (1997)
[18] Randolph, S. E.; Gern, L.; Nuttal, P. A., Co-feeding ticksepidemiological significance for tick-borne pathogen transmission, Parasitol. Today, 12, 472-479 (1996)
[19] Randolph, S. E.; Miklisova, D.; Lysy, J.; Rogers, D. J.; Labuda, M., Incidence from coincidencepatterns of tick infestations in rodents facilitate transmission of tick-borne encephalitis virus, Parasitology, 118, 177-186 (1999)
[20] Randolph, S. E.; Chemini, C.; Furlanello, C.; Genchi, C.; Hails, R. A.; Hudson, P. J.; Jones, L. D.; Medley, G.; Norman, R. A.; Rizzoli, A.; Smith, G.; Woolhouse, M. E.J., The ecology of tick-borne infections in wildlife reservoirs, ((Hudson, P. J.; Rizzoli, A.; Grenfell, B. T.; Hesterbeek, H.; Dobson, A. P., Ecology of Wildlife Diseases (2002), Oxford University Press: Oxford University Press Oxford), 119-138
[21] Sandberg, S.; Awerbuch, T. E.; Spielman, A., A comprehensive multiple matrix model for tick Lyme disease, J. Theor. Biol., 157, 203-220 (1992)
[22] Segel, L.; Slemrod, M., The quasi-steady-state assumptiona case study in perturbation, SIAM Rev., 31, 446-477 (1989) · Zbl 0679.34066
[23] Van Buskirk, J.; Ostfeld, R. S., Controlling Lyme disease by modifying the density and species composition of tick hosts, Ecol. Appl., 5, 1133-1140 (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.