Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability

Abstract This study explore the dynamics of malaria transmission utilizing a novel fractional nonlinear coupled malaria model with a beta derivative, intending to expand our understanding of the complex factors that drive disease spread. By using the General Exponential Rational Function Method (GER...

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Main Authors: Abdullah, Muhammad Shakeel, Shah Muhammad, Hameed Gul Ahmadzai
Format: Article
Language:English
Published: Nature Portfolio 2025-08-01
Series:Scientific Reports
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Online Access:https://doi.org/10.1038/s41598-025-12167-4
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author Abdullah
Muhammad Shakeel
Shah Muhammad
Hameed Gul Ahmadzai
author_facet Abdullah
Muhammad Shakeel
Shah Muhammad
Hameed Gul Ahmadzai
author_sort Abdullah
collection DOAJ
description Abstract This study explore the dynamics of malaria transmission utilizing a novel fractional nonlinear coupled malaria model with a beta derivative, intending to expand our understanding of the complex factors that drive disease spread. By using the General Exponential Rational Function Method (GERFM), the fractional nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, yielding a range of complex traveling wave solutions, including kink, anti-kink, and dark solitons. The physical behavior of these attained solutions is illustrated through detailed 2D and 3D graphs. The analysis shows key outcomes such as the occurrence of bifurcation analysis, quasi-periodic and chaotic patterns, as well as multi-stability and sensitivity within the model, underscoring the elaborate nature of malaria transmission dynamics. These findings offer new understanding into the modeling of disease spread and provide a strong structure for future research in malaria control. Finally, the study contributes to the development of more accurate predictive models with potential applications in the biomedical sciences, extending the role of fractional calculus in comprehension complex biological systems.
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institution Kabale University
issn 2045-2322
language English
publishDate 2025-08-01
publisher Nature Portfolio
record_format Article
series Scientific Reports
spelling doaj-art-802a2019905245c3a88aac9fbc6b2b3f2025-08-24T11:19:08ZengNature PortfolioScientific Reports2045-23222025-08-0115112510.1038/s41598-025-12167-4Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistabilityAbdullah0Muhammad Shakeel1Shah Muhammad2Hameed Gul Ahmadzai3School of Mathematics and Statistics, Central South UniversitySchool of Mathematics and Statistics, Central South UniversityDepartment of Mathematics, College of Science, King Saud UniversityPaktia UniversityAbstract This study explore the dynamics of malaria transmission utilizing a novel fractional nonlinear coupled malaria model with a beta derivative, intending to expand our understanding of the complex factors that drive disease spread. By using the General Exponential Rational Function Method (GERFM), the fractional nonlinear partial differential equations are transformed into nonlinear ordinary differential equations, yielding a range of complex traveling wave solutions, including kink, anti-kink, and dark solitons. The physical behavior of these attained solutions is illustrated through detailed 2D and 3D graphs. The analysis shows key outcomes such as the occurrence of bifurcation analysis, quasi-periodic and chaotic patterns, as well as multi-stability and sensitivity within the model, underscoring the elaborate nature of malaria transmission dynamics. These findings offer new understanding into the modeling of disease spread and provide a strong structure for future research in malaria control. Finally, the study contributes to the development of more accurate predictive models with potential applications in the biomedical sciences, extending the role of fractional calculus in comprehension complex biological systems.https://doi.org/10.1038/s41598-025-12167-4Fractional malaria modelBeta derivativeGeneralized exponential rational function methodTravelling wave solutionsQualitative dynamics analysis
spellingShingle Abdullah
Muhammad Shakeel
Shah Muhammad
Hameed Gul Ahmadzai
Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
Scientific Reports
Fractional malaria model
Beta derivative
Generalized exponential rational function method
Travelling wave solutions
Qualitative dynamics analysis
title Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
title_full Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
title_fullStr Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
title_full_unstemmed Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
title_short Complex travelling wave solutions of fractional nonlinear coupled malaria model: bifurcation, chaos, and multistability
title_sort complex travelling wave solutions of fractional nonlinear coupled malaria model bifurcation chaos and multistability
topic Fractional malaria model
Beta derivative
Generalized exponential rational function method
Travelling wave solutions
Qualitative dynamics analysis
url https://doi.org/10.1038/s41598-025-12167-4
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