The impact of hospital resources and environmental perturbations to the dynamics of SIRS model |
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| Authors: | Guijie Lan Sanling Yuan Baojun Song |
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| Institution: | 1. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China;2. Department of Applied Mathematics and Statistics, Montclair State University, Montclair, NJ 07043, USA;1. School of Mathematics and Statistics, Ningxia University, Yinchuan 750021, PR China;2. Department of Mathematics, University of Florida, Gainesville, FL 32611, USA;1. School of Mathematical Science, Huaiyin Normal University, Huaian 223300, China;2. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University Changchun, Jilin 130024, PR China;2. Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, King Abdulaziz University, Jeddah, Saudi Arabia;3. College of Science, China University of Petroleum Qingdao, Shandong 266580, PR China;4. Department of Mathematics, Quaid-i-Azam University, Islamabad 45320, Pakistan;1. School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun, Jilin 130024, PR China;2. School of Mathematics and Statistics, Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, PR China;3. Nonlinear Analysis and Applied Mathematics (NAAM) Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah 121589, Saudi Arabia;4. College of Science, China University of Petroleum (East China), Qingdao 266580, Shandong Province, PR China |
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| Abstract: | Incorporating the environmental perturbations and available resources of the public health system, we construct both deterministic and stochastic models of SIRS type. The deterministic model exhibits very rich dynamics, such as Hopf bifurcation and backward bifurcation which leads to the co-existence of the stable disease-free state and a stable endemic equilibrium. For the stochastic model, we show that under mild extra conditions, if the basic reproduction number is less than one, then the disease will be eradicated almost surely, and if the basic reproduction number is greater than one, the stochastic model will admit a unique ergodic stationary distribution, which implies that the disease persists almost surely. Part of our numerical simulations indicate that: (i) The introduction of environmental perturbations may drift the endemic equilibrium to the disease-free equilibrium, or vice versa; (ii) Increasing available resources is necessary in order to mitigate the infections. |
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