Global dynamics of a multi-stage brucellosis model with distributed delays and indirect transmission. (English) Zbl 1501.92160
Keywords:
brucellosis; multi-stage model; indirect transmission; global stability; Lyapunov functionalReferences:
| [1] | M.E. Meyer and M. Meagher, Brucellosis in freeranging bison (Bison bison) in Yellowstone, Grand Teton, and Wood Bu^Kalo National |
| [2] | M. Mustafa and P. Nicoletti, Proceedings of the Workshop on Guidelines for a Regional Brucellosis Control Program for the Middle East 14-17 February, Amman, Jordan, FAO, WHO and OIE, 1993. |
| [3] | M. Darwish and A. Benkirane, Field investigations of brucellosis in cattle and small ruminants in Syria, 1990-1996, Rev. Sci. Tech. OIE, 20(3) (2001), 769-775. |
| [4] | J.R. Ebright, T. Altantsetseg and R. Oyungerel, Emerging infectious diseases in Mongolia, Emerg. Infect. Dis., 9(12) (2003), 1509-1515. |
| [5] | G. Pappas, P. Papadimitriou, N. Akritidis, et al., The new global map of human brucellosis, Lancet Infect. Dis., 6 (2006), 91-99. |
| [6] | M. Corbel |
| [7] | J. McDermott, D. Grace and J. Zinsstag, Economics of brucellosis impact and control in lowincome countries, Rev. Sci. Tech., 32 (2013), 249-261. |
| [8] | M.J. Corbel, Brucellosis in humans and animals, WHO, FAO and OIE, 2006. |
| [9] | J. Parnas, W. Krüger and E. Tüppich, Die Brucellose des Menschen (Human Brucellosis), VEB VErlag Volk und Gesundheit, Berlin, 1966. |
| [10] | H. Krauss, A. Weber, B. Enders, et al., Zoonotic diseases, infection diseases transmitted from animals to human (Zoonosen, von Tier auf den Menschen übertragbare Infek-tionskrankheiten), Deutscher Ärzte-Verlag Köln, Cologne, 1996. |
| [11] | SCAHAW, Brucellosis in sheep and goats, Scientific Committee on Animal Health and Animal Welfare, 2001. |
| [12] | E.D. Ebel, M.S. Williams and S.M. Tomlinson, Estimating herd prevalence of bovine brucellosis in 46 U.S.A. states using slaughter surveillance, Prev. Vet. Med., 85 (2008), 295-316. |
| [13] | H.S. Lee, M. Her, M. Levine, et al. Time series analysis of human and bovine brucellosis in South Korea from 2005 to 2010, Prev. Vet. Med., 110 (2013), 190-197. |
| [14] | R.D. Jones, L. Kelly, T. England, et al., A quantitative risk assessment for the importation of brucellosis-infected breeding cattle into Great Britain from selected European countries, Prev. Vet. Med., 63 (2004), 51-61. |
| [15] | A.M. Al-Majali and M. Shorman, Childhood brucellosis in |
| [16] | P. Jia and A. Joyner, Human brucellosis occurrences in inner mongolia |
| [17] | J. González-Guzmán and R. Naulin, Analysis of a model of bovine brucellosis using singular perturbations, J. Math. Biol., 33 (1994), 211-234. · Zbl 0809.92019 |
| [18] | J.Zinsstag, F. Roth, D. Orkhon, et al., A model of animal-human brucellosis transmission in Mongolia, Prev. Vet. Med., 69 (2005), 77-95. |
| [19] | D. Andrew and M. Mary, The Population Dynamics of Brucellosis in the Yellowstone National Park, Ecology, 77(4) (1996), 1026-1036. |
| [20] | F. Xie and R.D. Horan, Disease and Behavioral Dynamics for Brucellosis Control in Elk and Cattle in the Greater Yellowstone Area, J. Agr. Resour. Econ., 34 (2009), 11-33. |
| [21] | D. Shabb, N. Chitnis, Z. Baljinnyam, et al., A mathematical model of the dynamics of Mongolian livestock populations, Livest. Sci., 157 (2013), 280-288. |
| [22] | B. AÏnseba, C. Benosman and P. Magal, A model for ovine brucellosis incorporating direct and indirect transmission, J. Biol. Dyn., 4(1) (2010), 2-11. · Zbl 1315.92072 |
| [23] | M.T. Li, G.Q. Sun, J. Zhang, et al., Transmission dynamics and control for a brucellosis model In Hinggan League of Inner Mongolia, China, Math. Biosci. Eng., 11 (2014), 1115-1137. · Zbl 1306.92061 |
| [24] | Q. Hou, X.D Sun, J. Zhang, et al., Modeling the Transmission Dynamics of Sheep Brucellosis in Inner Mongolia Autonomous Region, China, Math. Biosci., 242 (2013), 51-58. · Zbl 1257.92032 |
| [25] | Q. Hou, X.D. Sun, Y.M. Wang, et al., Global properties of a general dynamic model for animal |
| [26] | P.O. Lolika, C. Modnak and S. Mushayabasa, On the dynamics of brucellosis infection in bison population with vertical transmission and culling, Math. Biosci., 305 (2018), 42-54. · Zbl 1409.92244 |
| [27] | W.M. Liu, S.A. Levin and Y. Iwasa, Influence of nonlinear incidence rates upon the behavior of SIRS epidemiological models, J. Math. Biol., 23 (1986), 187-204. · Zbl 0582.92023 |
| [28] | H. McCallum, N. Barlow and J. Hone, How should pathogen transmission be modelled ?, Trends Ecol. Evol., 16(6) (2001), 295-300. |
| [29] | R. Breban, J.M Drake, D.E. Stallknecht, et al., The role of environmental transmission in recurrent avian influenza epidemics, PLoS Comput. Biol., 5(4) (2009), e1000346. |
| [30] | Z. Mukandavire, S. Liao, J. Wang, et al., Estimating the reproductive numbers for the 2008-2009 cholera outbreaks in Zimbabwe, Proc. Natl. Acad. Sci. USA, 108 (2011), 8767-8772. |
| [31] | H.B. Guo, M.Y. Li and Z.S. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72(1) (2012), 261-279. 33. J.P. LaSalle, Stability of Dynamical Systems, SIAM, Philadelphia, 1976. · Zbl 1244.34075 |
| [32] | 34. J.K. Hale and P. Waltman, Persistence in infinite-dimensional systems, SIAM J. Math. Anal., 20 (1989), 388-395. · Zbl 0692.34053 |
| [33] | 35. Y. Yang, L. Zou and S. Ruan, Global dynamics of a delayed within-host viral infection model with both virus-to-cell and cell-to-cell transmissions, Math. Biosci., 270 (2015), 183-191. · Zbl 1331.34160 |
| [34] | 36. O.P. Lolika and S. Mushayabasa, Dynamics and stability analysis of a brucellosis model with two discrete delays, Discrete Dyn. Nat. Soc., 2 (2018), 1-20. · Zbl 1417.92188 |
| [35] | 36. O.P. Lolika and S. Mushayabasa, Dynamics and stability analysis of a brucellosis model with two discrete delays, Discrete Dyn. Nat. Soc., 2 (2018), 1-20. · Zbl 1417.92188 |
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.
