Global behavior of solutions to an SI epidemic model with nonlinear diffusion in heterogeneous environment
In this paper, a nonlinear diffusion SI epidemic model with a general incidence rate in heterogeneous environment is studied. Global behavior of classical solutions under certain restrictions on the coefficients is considered. We first establish the global existence of classical solutions of the sys...
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Published in | AIMS mathematics Vol. 7; no. 4; pp. 6779 - 6791 |
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Format | Journal Article |
Language | English |
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AIMS Press
2022
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Abstract | In this paper, a nonlinear diffusion SI epidemic model with a general incidence rate in heterogeneous environment is studied. Global behavior of classical solutions under certain restrictions on the coefficients is considered. We first establish the global existence of classical solutions of the system under heterogeneous environment by energy estimate and maximum principles. Based on such estimates, we then study the large-time behavior of the solution of system under homogeneous environment. The model and mathematical results in [M. Kirane, S. Kouachi, Global solutions to a system of strongly coupled reaction-diffusion equations, Nonlinear Anal. , 26 (1996), 1387-1396.] are generalized. |
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AbstractList | In this paper, a nonlinear diffusion SI epidemic model with a general incidence rate in heterogeneous environment is studied. Global behavior of classical solutions under certain restrictions on the coefficients is considered. We first establish the global existence of classical solutions of the system under heterogeneous environment by energy estimate and maximum principles. Based on such estimates, we then study the large-time behavior of the solution of system under homogeneous environment. The model and mathematical results in [M. Kirane, S. Kouachi, Global solutions to a system of strongly coupled reaction-diffusion equations, Nonlinear Anal. , 26 (1996), 1387-1396.] are generalized. |
Author | Li, Xiaojuan Xu, Shenghu |
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Cites_doi | 10.1016/j.chaos.2021.110668 10.1016/0362-546x(94)00337-h 10.1016/j.jde.2004.01.004 10.1090/S0002-9939-07-08978-2 10.2307/2346882 10.1002/mma.6335 10.1016/j.nonrwa.2013.02.007 10.1002/mma.3078 10.1016/S0022-5193(89)80211-5 10.1016/j.jmaa.2008.01.089 10.1002/mma.2895 10.2307/1467324 10.1137/140981447 10.1112/plms.12276 10.1016/j.chaos.2020.109619 10.1016/j.aej.2021.10.008 10.1016/j.jmaa.2014.07.083 10.3934/cpaa.2017037 10.1017/S0956792518000463 10.1016/j.chaos.2019.109467 10.2307/3866 10.3389/fphy.2020.00064 10.1007/BF01215256 10.1016/j.jmaa.2017.05.058 10.3934/dcds.1998.4.193 10.1016/j.chaos.2020.110321 10.1016/j.nonrwa.2008.01.011 10.1142/9789812834744_0013 10.4039/entm9745fv 10.1016/j.amc.2010.06.052 10.3934/dcds.2004.10.719 10.2307/1936298 10.3934/dcdsb.2018176 10.1002/mma.6297 10.1016/j.amc.2013.11.090 10.1016/j.nonrwa.2010.08.029 10.1090/S0002-9939-05-07867-6 |
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