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Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis
This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis...
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Published in: | Fractal and fractional 2024-05, Vol.8 (5), p.299 |
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description | This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics. |
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The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.</description><identifier>ISSN: 2504-3110</identifier><identifier>EISSN: 2504-3110</identifier><identifier>DOI: 10.3390/fractalfract8050299</identifier><language>eng</language><publisher>Basel: MDPI AG</publisher><subject>Acquired immune deficiency syndrome ; AIDS ; Analysis ; Business competition ; Calculus ; COVID-19 vaccines ; Disease prevention ; Disease transmission ; Epidemiology ; existence and uniqueness ; Fixed points (mathematics) ; Forecasts and trends ; Fractal analysis ; Fractal geometry ; fractal-fractional derivative ; Fractals ; fractional Adams-Bashforth method ; Fractional calculus ; Functional analysis ; Health aspects ; HIV ; HIV (Viruses) ; HIV model ; Human immunodeficiency virus ; Immune system ; Infection ; Infections ; Mathematical models ; numerical simulation ; Population ; Qualitative analysis ; Simulation ; Simulation methods ; Stability ; Ulam-Hyers stability</subject><ispartof>Fractal and fractional, 2024-05, Vol.8 (5), p.299</ispartof><rights>COPYRIGHT 2024 MDPI AG</rights><rights>2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). Notwithstanding the ProQuest Terms and Conditions, you may use this content in accordance with the terms of the License.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><cites>FETCH-LOGICAL-c335t-ab1c7d3a517b2ffe0e8b643d0b8b3825e71f06f3d96eec456376221887ffc39d3</cites><orcidid>0000-0003-0342-491X ; 0000-0003-4515-8082</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.proquest.com/docview/3059417232/fulltextPDF?pq-origsite=primo$$EPDF$$P50$$Gproquest$$Hfree_for_read</linktopdf><linktohtml>$$Uhttps://www.proquest.com/docview/3059417232?pq-origsite=primo$$EHTML$$P50$$Gproquest$$Hfree_for_read</linktohtml><link.rule.ids>314,777,781,25734,27905,27906,36993,38497,43876,44571,74161,74875</link.rule.ids></links><search><creatorcontrib>Anjam, Yasir Nadeem</creatorcontrib><creatorcontrib>Turki Alqahtani, Rubayyi</creatorcontrib><creatorcontrib>Alharthi, Nadiyah Hussain</creatorcontrib><creatorcontrib>Tabassum, Saira</creatorcontrib><title>Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis</title><title>Fractal and fractional</title><description>This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. This proposed strategy offers a competitive advantage, enhancing comprehension of the model’s intricate dynamics.</description><subject>Acquired immune deficiency syndrome</subject><subject>AIDS</subject><subject>Analysis</subject><subject>Business competition</subject><subject>Calculus</subject><subject>COVID-19 vaccines</subject><subject>Disease prevention</subject><subject>Disease transmission</subject><subject>Epidemiology</subject><subject>existence and uniqueness</subject><subject>Fixed points (mathematics)</subject><subject>Forecasts and trends</subject><subject>Fractal analysis</subject><subject>Fractal geometry</subject><subject>fractal-fractional derivative</subject><subject>Fractals</subject><subject>fractional Adams-Bashforth method</subject><subject>Fractional calculus</subject><subject>Functional analysis</subject><subject>Health aspects</subject><subject>HIV</subject><subject>HIV (Viruses)</subject><subject>HIV model</subject><subject>Human immunodeficiency virus</subject><subject>Immune system</subject><subject>Infection</subject><subject>Infections</subject><subject>Mathematical models</subject><subject>numerical simulation</subject><subject>Population</subject><subject>Qualitative analysis</subject><subject>Simulation</subject><subject>Simulation methods</subject><subject>Stability</subject><subject>Ulam-Hyers stability</subject><issn>2504-3110</issn><issn>2504-3110</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2024</creationdate><recordtype>article</recordtype><sourceid>COVID</sourceid><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNptUttqGzEQXUoLDWm-oC-CPm-qy2ol9c2YpjG49CXpq9Bl5MqsV64km_rvo9ilFwgDc8ThzGGOmK57T_AtYwp_DNm4aqYzSMwxVepVd0U5HnpGCH79z_ttd1PKFmNMhWIci6tu_zgfIU5x3qD6A9Ay7fYT_Ir1hFJA96vv6CGbuexiKTHNn9BqrrDJpj7rvx6mGvs1HGFqfABXm6SgYzTo7rJSf8bGmgktWjuVWN51b4KZCtz8xuvu8e7zw_K-X3_7slou1r1jjNfeWOKEZ4YTYWkIgEHacWAeW2mZpBwECXgMzKsRwA18ZGKklEgpQnBMeXbdrS6-Ppmt3ue4M_mkk4n6TKS80SbX6CbQ0jhmOQneYz8EqZQnlivnwFoOIF3z-nDx2uf08wCl6m065BaoaIa5GoigjP5VbUwzjXNItcVvX-f0Qig-YCLGsaluX1C18rCLLs0QYuP_G2CXAZdTKRnCnzAE6-cD0C8cAHsCkgunaQ</recordid><startdate>20240501</startdate><enddate>20240501</enddate><creator>Anjam, Yasir Nadeem</creator><creator>Turki Alqahtani, Rubayyi</creator><creator>Alharthi, Nadiyah Hussain</creator><creator>Tabassum, Saira</creator><general>MDPI AG</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FE</scope><scope>8FG</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>COVID</scope><scope>DWQXO</scope><scope>HCIFZ</scope><scope>L6V</scope><scope>M7S</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PTHSS</scope><scope>DOA</scope><orcidid>https://orcid.org/0000-0003-0342-491X</orcidid><orcidid>https://orcid.org/0000-0003-4515-8082</orcidid></search><sort><creationdate>20240501</creationdate><title>Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis</title><author>Anjam, Yasir Nadeem ; Turki Alqahtani, Rubayyi ; Alharthi, Nadiyah Hussain ; Tabassum, Saira</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c335t-ab1c7d3a517b2ffe0e8b643d0b8b3825e71f06f3d96eec456376221887ffc39d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2024</creationdate><topic>Acquired immune deficiency syndrome</topic><topic>AIDS</topic><topic>Analysis</topic><topic>Business competition</topic><topic>Calculus</topic><topic>COVID-19 vaccines</topic><topic>Disease prevention</topic><topic>Disease transmission</topic><topic>Epidemiology</topic><topic>existence and uniqueness</topic><topic>Fixed points (mathematics)</topic><topic>Forecasts and trends</topic><topic>Fractal analysis</topic><topic>Fractal geometry</topic><topic>fractal-fractional derivative</topic><topic>Fractals</topic><topic>fractional Adams-Bashforth method</topic><topic>Fractional calculus</topic><topic>Functional analysis</topic><topic>Health aspects</topic><topic>HIV</topic><topic>HIV (Viruses)</topic><topic>HIV model</topic><topic>Human immunodeficiency virus</topic><topic>Immune system</topic><topic>Infection</topic><topic>Infections</topic><topic>Mathematical models</topic><topic>numerical simulation</topic><topic>Population</topic><topic>Qualitative analysis</topic><topic>Simulation</topic><topic>Simulation methods</topic><topic>Stability</topic><topic>Ulam-Hyers stability</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Anjam, Yasir Nadeem</creatorcontrib><creatorcontrib>Turki Alqahtani, Rubayyi</creatorcontrib><creatorcontrib>Alharthi, Nadiyah Hussain</creatorcontrib><creatorcontrib>Tabassum, Saira</creatorcontrib><collection>CrossRef</collection><collection>ProQuest SciTech Collection</collection><collection>ProQuest Technology Collection</collection><collection>Materials Science & Engineering Collection</collection><collection>ProQuest Central (Alumni Edition)</collection><collection>ProQuest Central</collection><collection>ProQuest Central Essentials</collection><collection>ProQuest Central</collection><collection>Technology Collection</collection><collection>ProQuest One Community College</collection><collection>Coronavirus Research Database</collection><collection>ProQuest Central Korea</collection><collection>SciTech Premium Collection</collection><collection>ProQuest Engineering Collection</collection><collection>Engineering Database</collection><collection>Publicly Available Content (ProQuest)</collection><collection>ProQuest One Academic Eastern Edition (DO NOT USE)</collection><collection>ProQuest One Academic</collection><collection>ProQuest One Academic UKI Edition</collection><collection>Engineering collection</collection><collection>DOAJ Directory of Open Access Journals</collection><jtitle>Fractal and fractional</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Anjam, Yasir Nadeem</au><au>Turki Alqahtani, Rubayyi</au><au>Alharthi, Nadiyah Hussain</au><au>Tabassum, Saira</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis</atitle><jtitle>Fractal and fractional</jtitle><date>2024-05-01</date><risdate>2024</risdate><volume>8</volume><issue>5</issue><spage>299</spage><pages>299-</pages><issn>2504-3110</issn><eissn>2504-3110</eissn><abstract>This article presents a non-linear deterministic mathematical model that captures the evolving dynamics of HIV disease spread, considering three levels of infection in a population. The model integrates fractal-fractional order derivatives using the Caputo operator and undergoes qualitative analysis to establish the existence and uniqueness of solutions via fixed-point theory. Ulam-Hyer stability is confirmed through nonlinear functional analysis, accounting for small perturbations. Numerical solutions are obtained using the fractional Adam-Bashforth iterative scheme and corroborated through MATLAB simulations. The results, plotted across various fractional orders and fractal dimensions, are compared with integer orders, revealing trends towards HIV disease-free equilibrium points for infective and recovered populations. Meanwhile, susceptible individuals decrease towards this equilibrium state, indicating stability in HIV exposure. The study emphasizes the critical role of controlling transmission rates to mitigate fatalities, curb HIV transmission, and enhance recovery rates. 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subjects | Acquired immune deficiency syndrome AIDS Analysis Business competition Calculus COVID-19 vaccines Disease prevention Disease transmission Epidemiology existence and uniqueness Fixed points (mathematics) Forecasts and trends Fractal analysis Fractal geometry fractal-fractional derivative Fractals fractional Adams-Bashforth method Fractional calculus Functional analysis Health aspects HIV HIV (Viruses) HIV model Human immunodeficiency virus Immune system Infection Infections Mathematical models numerical simulation Population Qualitative analysis Simulation Simulation methods Stability Ulam-Hyers stability |
title | Unveiling the Complexity of HIV Transmission: Integrating Multi-Level Infections via Fractal-Fractional Analysis |
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