| Summary: | 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.
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