Global dynamic behavior of a plant disease model with ratio dependent impulsive control strategy

Li, Wenjie; Huang, Lihong; Guo, Zhenyuan; Ji, Jinchen

doi:10.1016/j.matcom.2020.03.009

Cited by 16 publications

(1 citation statement)

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“…[9,12,21,25,28,34,41,45,46], H.C. [14,23,24] and I.C. [22,25,26,44] and the other control [1,3,10,18,40,42]. Nevertheless, in this manuscript, we design a SIR epidemic system to address the D.T.C.…”

Section: Introductionmentioning

confidence: 99%

Global dynamics and bifurcations of Filippov SIR epidemic model with general nonlinear transmission and discontinuous control

Alsaedi³

et al. 2023

Preprint

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This paper investigates the global dynamic behavior and bifurcations of a classical nonlinear transmission SIR epidemic model with discontinuous threshold strategy. Different from previous results, we not only consider the general nonlinear transmission, but also adopt the discontinuity control. First, the positivity and boundedness of the model are given. Second, by employing Lyapunov LaSalle approach and using Green Theorem, we perform the globally stable the three types of equilibria of the system. We analytically show the orbit can tend to the disease-free equilibrium point, the endemic equilibrium point or the sliding equilibrium point in discontinuous surfaces of the system. In addition, we also analyze the sliding bifurcations of the model when consider the special transmission. Finally, some numerical simulations are worked out to confirm the results obtained in this paper.

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