Dynamical analysis of a discrete-time SIR epidemic model |
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| Institution: | 1. School of Finance, Anhui University of Finance & Economics, Bengbu, Anhui 233030, PR China;2. Department of Mathematics, Faculty of Science, Fasa University, Fasa, Iran;1. College of Control Science and Engineering, Bohai University, Jinzhou 121013, China;2. School of Information Science and Engineering, Shandong Normal University, Jinan 250014, China;3. School of Control Science and Engineering, Tiangong University, Tianjin 300387, China;4. Faculty of Electronic Information and Electrical Engineering, Dalian University of Technology, Dalian 116024, China;5. Communication Systems and Networks Research Group, Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, Jeddah, Saudi Arabia;1. Department of Automation, Xiamen University, Xiamen, Fujian 361005, China;2. School of Systems Design and Intelligent Manufacturing, South University of Science and Technology, Shenzhen Guangdong 518000, China;1. School of Electrical Engineering, Anhui Polytechnic University, Wuhu241000, China;2. School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, Wuhan 430074, China;3. Department of Automation, University of Science and Technology of China, Hefei 230026, China;1. School of Automation, Nanjing University of Science and Technology, Nanjing, Jiangsu 210094, China;2. School of Automation, Southeast University, Nanjing, Jiangsu, 210096, China;1. School of Mechanical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China;2. Artiflcial Intelligence Institute of Industrial Technology, Nanjing Institute of Technology, Nanjing 211167, China |
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| Abstract: | In this paper, a discrete-time seasonally forced SIR epidemic model is investigated for different types of bifurcations. Although, many researchers already suggested numerically that this model can exhibit chaotic dynamics but not much focus is given to the bifurcation theory of the model. We prove analytically and numerically the existence of different types of bifurcations in the model. First, the one and two parameters bifurcations of this model are investigated by computing their critical normal form coefficients. Secondly, the flip, Neimark–Sacker, and strong resonances bifurcations are detected for this model. The critical coefficients identify the scenario associated with each bifurcation. The complete complex dynamical behavior of the model is investigated. Some graphical representations of the model are presented to verify the obtained results. |
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