1. DYNAMICAL BEHAVIOR OF AN SIR EPIDEMIC MODEL WITH RATIO-DEPENDENT IMPULSIVE CONTROL AND BEDDINGTON–DEANGELIS INCIDENCE.
- Author
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HUANG, RUILI, ZHANG, SUXIA, and XU, XIAXIA
- Subjects
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EPIDEMICS , *COMPUTER simulation , *EQUILIBRIUM , *COMPUTATIONAL neuroscience , *PHASE coding - Abstract
In this paper, we propose an epidemic model of SIR type with ratio-dependent impulse control and Beddington–DeAngelis (B–D) incidence. According to the magnitude of the basic reproductive number ℛ0 and the relation of the endemic equilibrium (S∗,I∗) and the ratio threshold h, dynamical analysis of the controlled system is conducted. Under the control strategy, if ℛ0 ≤ 1, the solutions converge to the disease-free equilibrium. If ℛ0 > 1 and I∗ S∗ > h, the impulsive system has periodic solution that is orbitally asymptotically stable, and order-k (k > 2) periodic solution does not exist. Furthermore, if ℛ0 > 1 and I∗ S∗ < h, the solution converges either to the endemic equilibrium or to a periodic solution, which is proved to be determined by the initial value. Finally, numerical simulations are performed to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]
- Published
- 2024
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