Transmission Dynamics of a High Dimensional Rabies Epidemic Model in a Markovian Random Environment

• Hao Peng ^[1] ; Qing Yang ^[1] ; Xinhong Zhang ^[1] ; Daqing Jiang ^[1]
  1. [1] China University of Petroleum

     China University of Petroleum

     China

     
• Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 21, Nº 2, 2022
• Idioma: inglés
• Enlaces
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• Resumen

  • This paper develops the spread dynamics of a 11-dimensional stochastic multi-host zoonotic model for the dog-CFB-human transmission of rabies, which is formulated as a piecewise deterministic Markov process. We firstly prove the existence of the global unique positive solution. Then we obtain sufficient conditions for the extinction and persistence of disease. One of the distinct features of this paper is that we prove the positive recurrence of the solution to the model by constructing a series of appropriate Lyapunov functions. Finally, numerical simulations are carried out to illustrate our theoretical results.

• Referencias bibliográficas
  • 1. CDC, Rabies-how is rabies transmitted? 2010, http://www.cdc.gov/rabies/transmission/index.html
  • 2. Tenzin, M.P.: Ward, review of rabies epidemiology and control in south, southeast and east Asia: past, present and prospects for elimination....
  • 3. Hampson, K., Dushoff, J., Bingham, J., Bruckner, G., Ali, Y., Dobson, A.: Synchronous cycles of domestic dog rabies in sub-saharan Africa...
  • 4. Zinsstag, J., Durr, S., Penny, M., Mindekem, R., Roth, F., Gonzalez, S., Naissengar, S., Hattendorf, J.: Transmission dynamic and economics...
  • 5. Anderson, R.M., Jackson, H.C., May, R.M., Smith, A.M.: Population dynamics of fox rabies in Europe. Nature 289, 765–771 (1981)
  • 6. Coyne, M.J., Smith, G., McAllister, F.E.: Mathematic model for the population biology of rabies in raccoons in the Mid-Atlantic states....
  • 7. Childs, J.E., Curns, A.T., Dey, M.E., Real, L.A., Feinstein, L., et al.: Predicting the local dynamics of epizootic rabies among raccoons...
  • 8. Clayton, T., Duke-Sylvester, S., Gross, L.J., Lenhart, S., Real, L.A.: Optimal control of a rabies epidemic model with a birth pulse. J....
  • 9. Allen, L.J.S., Flores, D.A., Ratnayake, R.K., Herbold, J.R.: Discrete-time deterministic and stochastic models for the spread of rabies....
  • 10. Artois, M., Langlais, M., Suppo, C.: Simulation of rabies control within an increasing fox population. Ecol. Model. 97, 23–34 (1997)
  • 11. Kallen, A., Arcuri, P., Murray, J.D.: A simple model for the spatial spread and control of rabies. J. Theor. Biol. 116, 377–393 (1985)
  • 12. Smith, D.L., Lucey, B., Waller, L.A., Childs, J.E., Real, L.A.: Predicting the spatial dynamics of rabies epidemic on heterogeneous landscapes....
  • 13. Huang, J., Ruan, S., Shu, Y., Wu, X.: Modeling the transmission dynamics of Rabies for Dog, Chinese Ferret Badger and human interactions...
  • 14. Liu, Q., Jiang, D.: Threshold behavior in a stochastic SIQR epidemic model with standard incidence and regime switching. Appl. Math. Comput....
  • 15. Wang, L., Jiang, D.: Ergodic property of the chemostat: a stochastic model under regime switching and with general response function....
  • 16. Settati, A., Lahrouz, A.: Stationary distribution of stochastic population systems under regime switching. Appl. Math. Comput. 244, 235–243...
  • 17. Zhang, X., Jiang, D., Ahmed, A., Hayat, T.: Stationary distribution of stochastic SIS epidemic model with vaccination under regime switching....
  • 18. Gray, A., Greenhalgh, D., Mao, X., Pan, J.: The SIS epidemic model with Markovian switching. J. Math. Anal. Appl. 394, 496–516 (2012)
  • 19. Mao, X.: Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79, 45–67 (1999)
  • 20. Mao, X., Marion, G., Renshaw, E.: Environmental Brownian noise suppresses explosions in population dynamics. Stochastic Process. Appl....
  • 21. Mao, X., Yuan, C.: Stochastic Differential Equations With Markovian Switching. Imperial College Press, London (2006)
  • 22. Ji, C., Jiang, D., Shi, N.: Multigroup SIR epidemic model with stochastic perturbation. Physica A. 390, 1747–1762 (2011)
  • 23. Berman, A., Plemmons, R.J.: Nonnegative Matrices in the Mathematical Sciences. Academic Press, New York (1979)
  • 24. Khasminskii, R., Zhu, C., Yin, G.: Stability of regime-switching diffusions. Stochastic Process. Appl. 117, 1037–1051 (2007)