Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays
We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pa...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2018-11, Vol.41 (16), p.6645-6672 |
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| creator | Elaiw, Ahmed M. AlShamrani, Noura H. |
| description | We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations. |
| doi_str_mv | 10.1002/mma.5182 |
| format | Article |
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We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. 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We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.</description><subject>adaptive immune response</subject><subject>Computer simulation</subject><subject>Dynamic stability</subject><subject>Functionals</subject><subject>global stability</subject><subject>Immunity</subject><subject>intracellular delay</subject><subject>Lyapunov function</subject><subject>Mathematical models</subject><subject>pathogen infection</subject><subject>Pathogens</subject><subject>Steady state</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp1kM1OwzAQhC0EEqUg8QiWuHBJ8TpOEx-rij-pFQfgwsVybIe6ipMQO1R5exzKldNKM9_ujgahayALIITeOScXGRT0BM2AcJ4Ay5enaEYgJwmjwM7Rhfd7QkgBQGfo4zXI0tY2jLitsGyw1LIL9ttg69zQTHonw679NA3WYyOdVR67VpsaH2zY4VoG06gxbmrshjrYrjY4unL0l-iskrU3V39zjt4f7t_WT8nm5fF5vdokivKUJrRgaU7SUjHOM1AVL7guYjjFdMwSDaOqippJyiVomZeMcJJlhpayXEKaztHN8W7Xt1-D8UHs26Fv4ktBgTIGBbCJuj1Sqm-9700lut462Y8CiJiaE7E5MTUX0eSIHmxtxn85sd2ufvkfIUBvhw</recordid><startdate>20181115</startdate><enddate>20181115</enddate><creator>Elaiw, Ahmed M.</creator><creator>AlShamrani, Noura H.</creator><general>Wiley Subscription Services, Inc</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><orcidid>https://orcid.org/0000-0001-5030-633X</orcidid></search><sort><creationdate>20181115</creationdate><title>Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays</title><author>Elaiw, Ahmed M. ; AlShamrani, Noura H.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2932-2843703bc49951cf989d8811c4dada03becff2e88117a1da7b409055e2bab6133</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>adaptive immune response</topic><topic>Computer simulation</topic><topic>Dynamic stability</topic><topic>Functionals</topic><topic>global stability</topic><topic>Immunity</topic><topic>intracellular delay</topic><topic>Lyapunov function</topic><topic>Mathematical models</topic><topic>pathogen infection</topic><topic>Pathogens</topic><topic>Steady state</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Elaiw, Ahmed M.</creatorcontrib><creatorcontrib>AlShamrani, Noura H.</creatorcontrib><collection>CrossRef</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><jtitle>Mathematical methods in the applied sciences</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Elaiw, Ahmed M.</au><au>AlShamrani, Noura H.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2018-11-15</date><risdate>2018</risdate><volume>41</volume><issue>16</issue><spage>6645</spage><epage>6672</epage><pages>6645-6672</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>We incorporate three distributed time delays into the model of pathogen dynamics with antibody and Cytotoxic T Lymphocyte (CTL) immune responses. We consider both actively and latently infected cells. The pathogen‐target incidence rate, production/proliferation, and removal rates of the cells and pathogens are represented by general nonlinear functions. We show that the solutions of the proposed model are nonnegative and ultimately bounded. We derive four threshold parameters that fully determine the existence and stability of the five steady states of the model. Using Lyapunov functionals, we established the global stability of the steady states of the model. The theoretical results are confirmed by numerical simulations.</abstract><cop>Freiburg</cop><pub>Wiley Subscription Services, Inc</pub><doi>10.1002/mma.5182</doi><tpages>28</tpages><orcidid>https://orcid.org/0000-0001-5030-633X</orcidid></addata></record> |
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| ispartof | Mathematical methods in the applied sciences, 2018-11, Vol.41 (16), p.6645-6672 |
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| language | eng |
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| source | Wiley Online Library Journals |
| subjects | adaptive immune response Computer simulation Dynamic stability Functionals global stability Immunity intracellular delay Lyapunov function Mathematical models pathogen infection Pathogens Steady state |
| title | Stability of an adaptive immunity pathogen dynamics model with latency and multiple delays |
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