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Sveir epidemiological model with varying infectivity and distributed delays

1. Department of Mathematics, Harbin Institute of Technology, Harbin 150001
2. Graduate School of Science and Technology, Shizuoka University, Hamamatsu 4328561
3. Graduate School of Science and Technology, Faculty of Engineering, Shizuoka University, Hamamatsu 432-8561
4. Academy of Fundamental and Interdisciplinary Sciences, Harbin Institute of Technology, 3041#, 2 Yi-Kuang Street, Harbin, 150080

## Abstract    Related pages

In this paper, based on an SEIR epidemiological model with distributed delays to account for varying infectivity, we introduce a vaccination compartment, leading to an SVEIR model. By employing direct Lyapunov method and LaSalle's invariance principle, we construct appropriate functionals that integrate over past states to establish global asymptotic stability conditions, which are completely determined by the basic reproduction number $\mathcal{R}_0^V$. More precisely, it is shown that, if $\mathcal{R}_0^V\leq 1$, then the disease free equilibrium is globally asymptotically stable; if $\mathcal{R}_0^V > 1$, then there exists a unique endemic equilibrium which is globally asymptotically stable. Mathematical results suggest that vaccination is helpful for disease control by decreasing the basic reproduction number. However, there is a necessary condition for successful elimination of disease. If the time for the vaccinees to obtain immunity or the possibility for them to be infected before acquiring immunity can be neglected, this condition would be satisfied and the disease can always be eradicated by some suitable vaccination strategies. This may lead to over-evaluating the effect of vaccination.
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Citation: Jinliang Wang, Gang Huang, Yasuhiro Takeuchi, Shengqiang Liu. Sveir epidemiological model with varying infectivity and distributed delays. Mathematical Biosciences and Engineering, 2011, 8(3): 875-888. doi: 10.3934/mbe.2011.8.875

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• 2. Asaf Khan, Gul Zaman, Optimal control strategy of SEIR endemic model with continuous age-structure in the exposed and infectious classes, Optimal Control Applications and Methods, 2018, 10.1002/oca.2437
• 3. Lili Liu, Xianning Liu, Global stability of an age-structured SVEIR epidemic model with waning immunity, latency and relapse, International Journal of Biomathematics, 2017, 10, 03, 1750038, 10.1142/S1793524517500383
• 4. Jinliang Wang, Min Guo, Xianning Liu, Zhitao Zhao, Threshold dynamics of HIV-1 virus model with cell-to-cell transmission, cell-mediated immune responses and distributed delay, Applied Mathematics and Computation, 2016, 291, 149, 10.1016/j.amc.2016.06.032
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• 8. Jinliang Wang, Ran Zhang, Toshikazu Kuniya, The dynamics of an SVIR epidemiological model with infection age: Table 1., IMA Journal of Applied Mathematics, 2016, 81, 2, 321, 10.1093/imamat/hxv039
• 9. Xinxin Tian, Jinliang Wang, Stability Analysis for Viral Infection Model with Multitarget Cells, Beddington-DeAngelis Functional Response, and Humoral Immunity, Discrete Dynamics in Nature and Society, 2015, 2015, 1, 10.1155/2015/654507
• 10. Lianwen Wang, Zhijun Liu, Xingan Zhang, Global dynamics of an SVEIR epidemic model with distributed delay and nonlinear incidence, Applied Mathematics and Computation, 2016, 284, 47, 10.1016/j.amc.2016.02.058