Solving age-dependent infectious diseases and tumor growth models using the contraction approach
This study establishes existence and uniqueness theorems for solution sets in three domains of biological modeling: age-dependent diseases infectiousness, infectious disease transmission, and tumor growth dynamics. We illustrate that fixed-point theory, using contraction mapping concepts, offers sol...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-12-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016125003504 |
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| author | Syed Khayyam Shah Muhammad Sarwar Kamal Shah Manel Hleili Thabet Abdeljawad |
| author_facet | Syed Khayyam Shah Muhammad Sarwar Kamal Shah Manel Hleili Thabet Abdeljawad |
| author_sort | Syed Khayyam Shah |
| collection | DOAJ |
| description | This study establishes existence and uniqueness theorems for solution sets in three domains of biological modeling: age-dependent diseases infectiousness, infectious disease transmission, and tumor growth dynamics. We illustrate that fixed-point theory, using contraction mapping concepts, offers solid mathematical foundations for model stability and solution consistency. Our principal contribution is to develop generalized contraction techniques that ensure the existence and uniqueness of solutions for the differential equations describing these biological systems. This mathematical framework improves the mathematical proficiency of epidemiological and oncological modeling and offers computational techniques for model validation. These findings address significant deficiencies in the scientific literature by employing fixed-point methodologies from classical analysis to manage the intricate nonlinearities present in biological systems, thereby paving emerging paths for the investigation of disease dynamics and treatment effectiveness. • Purpose: In this work, we will look for the criteria of existence of unique solutions of the equations in the models like, tumor growth, infectious diseases dependency and spread. • Methodology: Utilizing contraction principle and using different contractions from the literature like, F-contraction, α-F-contraction, rational type (ψ, φ)-contraction, and Geraghty-type contraction we come up with the conditions where the mentioned biological models possesses unique solutions. • Findings: Imposing different conditions we established novel results which help us ensure the stability by analyzing the existence and uniqueness of the solution of the problems arising in the aforementioned biological models. |
| format | Article |
| id | doaj-art-2ca12c6f4eb6467180d2be3663a5a31b |
| institution | DOAJ |
| issn | 2215-0161 |
| language | English |
| publishDate | 2025-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj-art-2ca12c6f4eb6467180d2be3663a5a31b2025-08-20T02:56:32ZengElsevierMethodsX2215-01612025-12-011510350510.1016/j.mex.2025.103505Solving age-dependent infectious diseases and tumor growth models using the contraction approachSyed Khayyam Shah0Muhammad Sarwar1Kamal Shah2Manel Hleili3Thabet Abdeljawad4Department of Sustainable Environment and Energy Systems (SEES), Middle East Technical University, Northern Cyprus Campus, 99738 Kalkanli, Guzelyurt, Mersin 10, TurkeyDepartment of Mathematics, University of Malakand, Chakdara Dir(L), 18000, Khyber, Pakhtunkhwa, Pakistan; Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Corresponding authors.Department of mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi Arabia; Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of mathematics, Faculty of Science, University of Tabuk, P.O. Box 741, Tabuk 71491, Saudi ArabiaDepartment of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Saveetha University, Chennai 602105, Tamil Nadu, India; Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Garankuwa, Medusa 0204, South Africa; Corresponding authors.This study establishes existence and uniqueness theorems for solution sets in three domains of biological modeling: age-dependent diseases infectiousness, infectious disease transmission, and tumor growth dynamics. We illustrate that fixed-point theory, using contraction mapping concepts, offers solid mathematical foundations for model stability and solution consistency. Our principal contribution is to develop generalized contraction techniques that ensure the existence and uniqueness of solutions for the differential equations describing these biological systems. This mathematical framework improves the mathematical proficiency of epidemiological and oncological modeling and offers computational techniques for model validation. These findings address significant deficiencies in the scientific literature by employing fixed-point methodologies from classical analysis to manage the intricate nonlinearities present in biological systems, thereby paving emerging paths for the investigation of disease dynamics and treatment effectiveness. • Purpose: In this work, we will look for the criteria of existence of unique solutions of the equations in the models like, tumor growth, infectious diseases dependency and spread. • Methodology: Utilizing contraction principle and using different contractions from the literature like, F-contraction, α-F-contraction, rational type (ψ, φ)-contraction, and Geraghty-type contraction we come up with the conditions where the mentioned biological models possesses unique solutions. • Findings: Imposing different conditions we established novel results which help us ensure the stability by analyzing the existence and uniqueness of the solution of the problems arising in the aforementioned biological models.http://www.sciencedirect.com/science/article/pii/S2215016125003504Fixed pointInfectious diseaseTumorDifferential equationsIntegral equations |
| spellingShingle | Syed Khayyam Shah Muhammad Sarwar Kamal Shah Manel Hleili Thabet Abdeljawad Solving age-dependent infectious diseases and tumor growth models using the contraction approach MethodsX Fixed point Infectious disease Tumor Differential equations Integral equations |
| title | Solving age-dependent infectious diseases and tumor growth models using the contraction approach |
| title_full | Solving age-dependent infectious diseases and tumor growth models using the contraction approach |
| title_fullStr | Solving age-dependent infectious diseases and tumor growth models using the contraction approach |
| title_full_unstemmed | Solving age-dependent infectious diseases and tumor growth models using the contraction approach |
| title_short | Solving age-dependent infectious diseases and tumor growth models using the contraction approach |
| title_sort | solving age dependent infectious diseases and tumor growth models using the contraction approach |
| topic | Fixed point Infectious disease Tumor Differential equations Integral equations |
| url | http://www.sciencedirect.com/science/article/pii/S2215016125003504 |
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