Modeling disease transmission in a mixed-species grazing environment

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In this article, we propose and analyzed a model describes the dynamics of a disease affects two different herbivores populations co-grazing together in the same environment under vaccination strategies and cross-immunity between the two species. Results show that the disease free equilibrium point (DFE) is locally asymptotically stable when the basic reproduction number, R0, is less than unity, and unstable when R0 is greater than unity, and our model undergoes a backward bifurcation, where R0 < 1 is not sufficient for the disease elimination, as R0 passes throw unity. Numerical results show that cross-immunity plays an important role in the eradication of the disease from both populations, however it plays also a negative role for both populations in the presence of vaccination strategies.

Original languageEnglish
Article number7
JournalCommunications in Mathematical Biology and Neuroscience
Publication statusPublished - 2017


  • Basic reproduction number
  • Cross-immunity
  • Mixed-species grazing
  • Numerical simulation
  • Vaccination

ASJC Scopus subject areas

  • General Neuroscience
  • General Biochemistry,Genetics and Molecular Biology
  • Applied Mathematics


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