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Global dynamics of multi-group SEI animal disease models with indirect transmission

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  • Wang, Yi
  • Cao, Jinde

Abstract

A challenge to multi-group epidemic models in mathematical epidemiology is the exploration of global dynamics. Here we formulate multi-group SEI animal disease models with indirect transmission via contaminated water. Under biologically motivated assumptions, the basic reproduction number R0 is derived and established as a sharp threshold that completely determines the global dynamics of the system. In particular, we prove that if R0<1, the disease-free equilibrium is globally asymptotically stable, and the disease dies out; whereas if R0>1, then the endemic equilibrium is globally asymptotically stable and thus unique, and the disease persists in all groups. Since the weight matrix for weighted digraphs may be reducible, the afore-mentioned approach is not directly applicable to our model. For the proofs we utilize the classical method of Lyapunov, graph-theoretic results developed recently and a new combinatorial identity. Since the multiple transmission pathways may correspond to the real world, the obtained results are of biological significance and possible generalizations of the model are also discussed.

Suggested Citation

  • Wang, Yi & Cao, Jinde, 2014. "Global dynamics of multi-group SEI animal disease models with indirect transmission," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 81-89.
    • Handle: RePEc:eee:chsofr:v:69:y:2014:i:c:p:81-89
    DOI: 10.1016/j.chaos.2014.09.009
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    References listed on IDEAS

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    1. Li, Guihua & Wang, Wendi & Jin, Zhen, 2006. "Global stability of an SEIR epidemic model with constant immigration," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 1012-1019.
    2. Li, Guihua & Jin, Zhen, 2005. "Global stability of a SEIR epidemic model with infectious force in latent, infected and immune period," Chaos, Solitons & Fractals, Elsevier, vol. 25(5), pages 1177-1184.
    3. Li, Guihua & Zhen, Jin, 2005. "Global stability of an SEI epidemic model with general contact rate," Chaos, Solitons & Fractals, Elsevier, vol. 23(3), pages 997-1004.
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    2. Ullah, Saif & Khan, Muhammad Altaf & Farooq, Muhammad & Gul, Taza, 2019. "Modeling and analysis of Tuberculosis (TB) in Khyber Pakhtunkhwa, Pakistan," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 181-199.

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