An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model
This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of...
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| Veröffentlicht in: | Journal of applied mathematics & computing 2021, Vol.67 (1-2), p.707-730 |
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| container_title | Journal of applied mathematics & computing |
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| creator | Wang, Xingyu Liu, Zhijun Wang, Lianwen Guo, Caihong Xiang, Huili |
| description | This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity. |
| doi_str_mv | 10.1007/s12190-020-01487-5 |
| format | Article |
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Appl. Math. Comput</addtitle><addtitle>J Appl Math Comput</addtitle><description>This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. It is concluded that joint implementation of these measures can minimize the numbers of exposed and infectious individuals in the shortest time, so it is the most efficient strategy to curb the hepatitis B epidemic. Moreover, vaccination for newborns plays the core role and maintains the high level of population immunity.</description><subject>Applied mathematics</subject><subject>Computational Mathematics and Numerical Analysis</subject><subject>Differential equations</subject><subject>Differential geometry</subject><subject>Dynamic stability</subject><subject>Epidemics</subject><subject>Hepatitis</subject><subject>Hepatitis B</subject><subject>Immunity</subject><subject>Mathematical and Computational Engineering</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Mathematics of Computing</subject><subject>Optimal control</subject><subject>Original Research</subject><subject>Stability criteria</subject><subject>Theory of Computation</subject><issn>1598-5865</issn><issn>1865-2085</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp9kU1vFSEUhidGY2v1D7gwJG7cjPI5wMakaao2adJFW7cEmDNXGgZGmNuk_16ut60fiy4IhPc5L-fwdt1bgj8SjOWnSijRuMe0LcKV7MWz7pCoQfQUK_G8nYVWvWgXB92rWm8wHqTG-mV3wJhQnAz0sEvHCdllicHbNeSE8oQsSvkWItpAnmEtwSNfwgplJ68ZbWJ2NvZ1tS7EsN6hpWQXYa4PtSmGBLagy9Oz75cIljDC3EzmPEJ83b2YbKzw5n4_6q6_nF6dfOvPL76enRyf955LvvajpUxbobUHatU4WucV54J6iT11gN3AtcOUweD0MLEJ3IQbpZwE2T5AsqPu89532boZRg9pLTaapYTZljuTbTD_Kin8MJt8a6QaNGesGXy4Nyj55xbqauZQPcRoE-RtNZQrPeBBEdLQ9_-hN3lbUhvPUCEJVkSRXUd0T_mSay0wPTZDsNnFafZxmhan-R2nEa3o3d9jPJY85NcAtgdqk9IGyp-3n7D9BeSKrUY</recordid><startdate>2021</startdate><enddate>2021</enddate><creator>Wang, Xingyu</creator><creator>Liu, Zhijun</creator><creator>Wang, Lianwen</creator><creator>Guo, Caihong</creator><creator>Xiang, Huili</creator><general>Springer Berlin Heidelberg</general><general>Springer Nature B.V</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>7X8</scope><scope>5PM</scope><orcidid>https://orcid.org/0000-0002-9914-9627</orcidid></search><sort><creationdate>2021</creationdate><title>An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model</title><author>Wang, Xingyu ; Liu, Zhijun ; Wang, Lianwen ; Guo, Caihong ; Xiang, Huili</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c474t-da239a599ce2a8ddabc84452c70c2be0b649b023e6b96f3febf0dda8b7e718673</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>Applied mathematics</topic><topic>Computational Mathematics and Numerical Analysis</topic><topic>Differential equations</topic><topic>Differential geometry</topic><topic>Dynamic stability</topic><topic>Epidemics</topic><topic>Hepatitis</topic><topic>Hepatitis B</topic><topic>Immunity</topic><topic>Mathematical and Computational Engineering</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Mathematics of Computing</topic><topic>Optimal control</topic><topic>Original Research</topic><topic>Stability criteria</topic><topic>Theory of Computation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Wang, Xingyu</creatorcontrib><creatorcontrib>Liu, Zhijun</creatorcontrib><creatorcontrib>Wang, Lianwen</creatorcontrib><creatorcontrib>Guo, Caihong</creatorcontrib><creatorcontrib>Xiang, Huili</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><collection>MEDLINE - Academic</collection><collection>PubMed Central (Full Participant titles)</collection><jtitle>Journal of applied mathematics & computing</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Wang, Xingyu</au><au>Liu, Zhijun</au><au>Wang, Lianwen</au><au>Guo, Caihong</au><au>Xiang, Huili</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model</atitle><jtitle>Journal of applied mathematics & computing</jtitle><stitle>J. Appl. Math. Comput</stitle><addtitle>J Appl Math Comput</addtitle><date>2021</date><risdate>2021</risdate><volume>67</volume><issue>1-2</issue><spage>707</spage><epage>730</epage><pages>707-730</pages><issn>1598-5865</issn><eissn>1865-2085</eissn><abstract>This work applies a novel geometric criterion for nonlinear autonomous differential equations developed by Lu and Lu (NARWA 36:20–43, 2017) to a nonlinear SEIVS epidemic model with temporary immunity and achieves its threshold dynamics. Specifically, global-stability problems for the SEIVS model of Cai and Li (AMM 33:2919–2926, 2009) are effectively solved. The corresponding optimal control system with vaccination, awareness campaigns and treatment is further established and four different control strategies are compared by numerical simulations to contain hepatitis B. 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| subjects | Applied mathematics Computational Mathematics and Numerical Analysis Differential equations Differential geometry Dynamic stability Epidemics Hepatitis Hepatitis B Immunity Mathematical and Computational Engineering Mathematical models Mathematics Mathematics and Statistics Mathematics of Computing Optimal control Original Research Stability criteria Theory of Computation |
| title | An application of a novel geometric criterion to global-stability problems of a nonlinear SEIVS epidemic model |
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