Global analysis for a delayed SIV model with direct and environmental transmissions |
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| Authors: | Tongqian Zhan Xinzhu Meng and Tonghua Zhang |
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| Institution: | College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China;State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P.R.China,College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, P. R. China;State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, P.R.China and Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122, Australia |
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| Abstract: | In this paper, we propose a new SIV epidemic model with time delay, which also involves both direct and environmental transmissions. For such model, we first introduce the basic reproduction number $\mathscr{R}$ by using the next generation matrix. And then global stability of the equilibria is discussed by means of Lyapunov
functionals and LaSalle''s invariance principle for delay differential equations, which shows that the infection-free equilibrium of the system is globally asymptotically stable if $\mathscr{R}<1$ and the epidemic equilibrium of the system is globally asymptotically stable for $\m |
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| Keywords: | Global stability environmental transmission time delay Lyapunov functional |
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