CHAOTIC EFFECTS ON DISEASE SPREAD IN A SIMPLE ECO-EPIDEMIOLOGICAL SYSTEM

Junyuan Yang; Maia Martcheva; Zhen Jin

doi:10.11948/2017072

2017 Volume 7 Issue 3

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Junyuan Yang, Maia Martcheva, Zhen Jin. CHAOTIC EFFECTS ON DISEASE SPREAD IN A SIMPLE ECO-EPIDEMIOLOGICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1161-1176. doi: 10.11948/2017072

Citation:

Junyuan Yang, Maia Martcheva, Zhen Jin. CHAOTIC EFFECTS ON DISEASE SPREAD IN A SIMPLE ECO-EPIDEMIOLOGICAL SYSTEM[J]. Journal of Applied Analysis & Computation, 2017, 7(3): 1161-1176. doi: 10.11948/2017072

CHAOTIC EFFECTS ON DISEASE SPREAD IN A SIMPLE ECO-EPIDEMIOLOGICAL SYSTEM

1 Complex Systems Research Center, Shanxi University, Shanxi, 030006 Taiyuan, China;
2 School of Mathematics, Shanxi University, Shanxi, 030006 Taiyuan, China;
3 Department of Mathematics, University of Florida, FL, 32611-8105 Gainesville, USA

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Abstract

Abstract

In this paper, an eco-epidemiological model where prey disease is structured as a susceptible-infected model is investigated. Thresholds that control disease spread and population persistence are obtained. Existence, stability and instability of the system are studied. Hopf bifurcation is shown to occur where a periodic solution bifurcates from the coexistence equilibrium. Simulations show that the system exhibits chaotic phenomena when the transmission rate is varied.
- Eco-epidemiological /
- Hopf bifurcation /
- chaos
MSC: 92D30;92D25

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References

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