Nonlinear state-dependent feedback control strategy in the SIR epidemic model with resource limitation

Advances in Difference Equations

Lin Fei Nie¹  Ji Gang Li²  Zhi Long He²  Zhen Zhao³ 

[1] College of Mathematics and Systems Science, Xinjiang University;School of Finance, Xinjiang University of Finance and Economics;School of Statistics and Information, Xinjiang University of Finance and Economics;

关键词: SIR model;    nonlinear state-dependent impulsive function;    periodic solution;    orbital stability;    chaotic solution;   

DOI  :  10.1186/s13662-017-1229-8

来源: DOAJ

【 摘 要 】

Abstract In present work, in order to avoid the spread of disease, the impulse control strategy is implemented to keep the density of infections at a low level. The SIR epidemic model with resource limitation including a nonlinear impulsive function and a state-dependent feedback control scheme is proposed and analyzed. Based on the qualitative properties of the corresponding continuous system, the existence and stability of positive order-k ( k ∈ Z + $k\in\mathbf{Z}^{+}$ ) periodic solution are investigated. By using the Poincaré map and the geometric method, some sufficient conditions for the existence and stability of positive order-1 or order-2 periodic solution are obtained. Moreover, the sufficient conditions which guarantee the nonexistence of order-k ( k ≥ 3 $k\geq3$ ) periodic solution are given. Some numerical simulations are carried out to illustrate the feasibility of our main results.

【 授权许可】

Unknown