Mathematical Biosciences and Engineering

2020, Issue 5: 5849-5863. doi: 10.3934/mbe.2020312
Research article

Dynamic behavior of swine influenza transmission during the breed-slaughter process

• Received: 20 May 2020 Accepted: 24 August 2020 Published: 02 September 2020
• Global influenza pandemics have brought about various public health crises, such as the 2009 H1N1 swine flu. Actually, most swine influenza infections occur during the breed-slaughter process. However, there is little research about the mathematical model to elaborate on the swine influenza transmission with human-pig interaction. In this paper, a new breed-slaughter model with swine influenza transmission is proposed, and the equilibrium points of the model are calculated subsequently. Meanwhile, we analyze the existence of the equilibrium points by the persistence theory, and discuss their stability by the basic reproduction number. And then, we focus on the invasion process of infected domestic animals into the habitat of humans. Under certain conditions as in Theorem 2, we construct a propagating terrace linking human habitat to animal-human coexistent habitat, then to swine flu natural foci, which is divided by spreading speeds.

Citation: Fangyuan Chen, Rong Yuan. Dynamic behavior of swine influenza transmission during the breed-slaughter process[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5849-5863. doi: 10.3934/mbe.2020312

Related Papers:

• Global influenza pandemics have brought about various public health crises, such as the 2009 H1N1 swine flu. Actually, most swine influenza infections occur during the breed-slaughter process. However, there is little research about the mathematical model to elaborate on the swine influenza transmission with human-pig interaction. In this paper, a new breed-slaughter model with swine influenza transmission is proposed, and the equilibrium points of the model are calculated subsequently. Meanwhile, we analyze the existence of the equilibrium points by the persistence theory, and discuss their stability by the basic reproduction number. And then, we focus on the invasion process of infected domestic animals into the habitat of humans. Under certain conditions as in Theorem 2, we construct a propagating terrace linking human habitat to animal-human coexistent habitat, then to swine flu natural foci, which is divided by spreading speeds.

 [1] E. Giuffra, J. M. H. Kijas, V. Amarger, O. Carlborg, J. T. Jeon, L. Andersson, The origin of the domestic pig: Independent domestication and subsequent introgression, Genetics, 154 (2000), 1785-1791. [2] J. S. Mackenzie, M. Jeggo, P. Daszak, J. A. Richt, One Health: The human-animal-environment interfaces in emerging infectious diseases, Springer, (2013). [3] B. J. Coburn, C. Cosner, S. Ruan, Emergence and dynamics of influenza super-strains, BMC Public Health, 11 (2011), 597-615. [4] J. Murray, Mathematical Biology: I. An Introduction, Springer, (2013). [5] H. Thieme, Persistence under relaxed point-dissipativity (with application to an endemic model), SIAM J. Math. Anal., 24 (1993),407-435. [6] A. Pugliese, Population models for disease with no recovery, J. Math. Biol., 28 (1990) 65-82. [7] J. Zhou, H. W. Hethcote, Population size dependent incidence in models for diseases without immunity, J. Math. Biol., 32 (1994), 809-834. [8] H. Hu, L. Xu, K. Wang, A comparison of deterministic and stochastic predator-prey models with disease in the predator, Discrete Cont. Dyn. B, 24 (2018), 2837-2863. [9] L. Han, A. Pugliese, Epidemics in two competing species, Nonlinear Anal. Real World Appl., 10 (2009), 723-744. [10] P. Magal, X. Zhao, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37 (2005), 251-275. [11] P. Dreessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, SIAM J. Math. Anal., 180 (2002), 29-48. [12] O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio r0 in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382. [13] J. Hofbauer, K. Sigmund, The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection, Cambridge University Press, (1988). [14] D. G. Aronson, H. F. Weinberger, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, in Partial Differential Equations And Related Topics, Springer, (1975), 5-49. [15] C. Carrère, Spreading speeds for a two-species competition-diffusion system, J. Differ. Equations, 264 (2018), 2133-2156. [16] Y. Kan-On, Parameter dependence of propagation speed of travelling waves for competitiondiffusion equations, SIAM J. Math. Anal., 26 (1995), 340-363. [17] M. A. Lewis, B. Li, H. F. Weinberger, Spreading speed and linear determinacy for two-species competition models, J. Math. Biol., 45 (2002), 219-233. [18] H. F. Weinberger, M. A. Lewis, B. Li, Analysis of linear determinacy for spread in cooperative models, J. Math. Biol. 45 (2002), 183-218. [19] G. Lin, Spreading speeds of a lotka-volterra predator-prey system: the role of the predator, Nonlinear Anal. Theory Methods Appl., 74 (2011), 2448-2461. [20] G. Lin, W. T. Li, Asymptotic spreading of competition diffusion systems: The role of interspecific competitions, Eur. J. Appl. Math., 23 (2012), 669-689. [21] C. C. Wu, The spreading speed for a predator-prey model with one predator and two preys, Appl. Math. Lett. 91 (2019), 9-14. [22] H. Wang, X. S. Wang, Traveling wave phenomena in a kermack-mckendrick sir model, J. Dyn. Differ. Equations, 28 (2016), 143-166.
通讯作者: 陈斌, bchen63@163.com
• 1.

沈阳化工大学材料科学与工程学院 沈阳 110142

1.285 1.3

Article outline

Figures(5)

• On This Site