A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections
In this paper, we propose a fractional‐order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation a...
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| Veröffentlicht in: | Mathematical methods in the applied sciences 2021-07, Vol.44 (10), p.8011-8025 |
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| container_title | Mathematical methods in the applied sciences |
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| creator | Chinnathambi, Rajivganthi Rihan, Fathalla A. Alsakaji, Hebatallah J. |
| description | In this paper, we propose a fractional‐order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. We investigate the qualitative behaviors of the model throughout the local stability of the steady states and bifurcation analysis. A discrete time delay is introduced in the model to justify the time taken for diagnosis of the disease. Existence and positivity of the solutions are investigated. Some interesting sufficient conditions that ensure the local asymptotic stability of infection‐free and endemic steady states are studied. The fractional‐order TB model undergoes Hopf bifurcation with respect to time delay and disease transmission rate. The presence of fractional order and time delay in the model improves the model behaviors and develops the stability results. A numerical example is provided to support our theoretical results. |
| doi_str_mv | 10.1002/mma.5676 |
| format | Article |
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A numerical example is provided to support our theoretical results.</description><subject>bifurcation</subject><subject>Disease control</subject><subject>fractional order</subject><subject>Hopf bifurcation</subject><subject>stability</subject><subject>Stability analysis</subject><subject>Steady state</subject><subject>time delay</subject><subject>Time lag</subject><subject>Tuberculosis</subject><issn>0170-4214</issn><issn>1099-1476</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2021</creationdate><recordtype>article</recordtype><recordid>eNp1kE1OwzAQRi0EEqUgcQRLbNikjGMnTpZVxZ_Uig2srUlsQ6okLnYCdMcROCMnIWmRWLEazczTN5pHyDmDGQOIr5oGZ0kq0wMyYZDnERMyPSQTYBIiETNxTE5CWANAxlg8IWFOrceyq1yL9ffnl_PaeNo4bWr6XnUvtKsaQ4cOt9Q6T7u-ML7saxeqsAdMq92zaV0fqDdj0huOaRRbTc3H36pqrdndCafkyGIdzNlvnZKnm-vHxV20fLi9X8yXURnnPI14lmvIOObCpqZEFCVmKIELCRJ5gUwUoFHyzGZJyoqE57IcZpnmIGLQlk_JxT53491rb0Kn1q73w59BxQlPU54nsRioyz1VeheCN1ZtfNWg3yoGalSqBqVqVDqg0R59r2qz_ZdTq9V8x_8AbiN6iw</recordid><startdate>20210715</startdate><enddate>20210715</enddate><creator>Chinnathambi, Rajivganthi</creator><creator>Rihan, Fathalla A.</creator><creator>Alsakaji, Hebatallah J.</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/0000-0003-3855-5944</orcidid><orcidid>https://orcid.org/0000-0002-9386-2173</orcidid></search><sort><creationdate>20210715</creationdate><title>A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections</title><author>Chinnathambi, Rajivganthi ; Rihan, Fathalla A. ; Alsakaji, Hebatallah J.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c2936-389d083a94f6ecaa4ca8a7034707a3ba14b0da738f8561b5397c14b8d30420df3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2021</creationdate><topic>bifurcation</topic><topic>Disease control</topic><topic>fractional order</topic><topic>Hopf bifurcation</topic><topic>stability</topic><topic>Stability analysis</topic><topic>Steady state</topic><topic>time delay</topic><topic>Time lag</topic><topic>Tuberculosis</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Chinnathambi, Rajivganthi</creatorcontrib><creatorcontrib>Rihan, Fathalla A.</creatorcontrib><creatorcontrib>Alsakaji, Hebatallah J.</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>Chinnathambi, Rajivganthi</au><au>Rihan, Fathalla A.</au><au>Alsakaji, Hebatallah J.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections</atitle><jtitle>Mathematical methods in the applied sciences</jtitle><date>2021-07-15</date><risdate>2021</risdate><volume>44</volume><issue>10</issue><spage>8011</spage><epage>8025</epage><pages>8011-8025</pages><issn>0170-4214</issn><eissn>1099-1476</eissn><abstract>In this paper, we propose a fractional‐order delay differential model for tuberculosis (TB) transmission with the effects of endogenous reactivation and exogenous reinfections. 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| source | Wiley Online Library Journals Frontfile Complete |
| subjects | bifurcation Disease control fractional order Hopf bifurcation stability Stability analysis Steady state time delay Time lag Tuberculosis |
| title | A fractional‐order model with time delay for tuberculosis with endogenous reactivation and exogenous reinfections |
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