A new epidemic model of sexually transmittable diseases: a fractional numerical approach
Abstract This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in p...
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Nature Portfolio
2025-01-01
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| Online Access: | https://doi.org/10.1038/s41598-025-87385-x |
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| author | Mudassar Rafique Muhammad Aziz Ur Rehamn Aisha M. Alqahtani Muhammad Rafiq A. F. Aljohani Zafar Iqbal Nauman Ahmed Shafiullah Niazai Ilyas Khan |
| author_facet | Mudassar Rafique Muhammad Aziz Ur Rehamn Aisha M. Alqahtani Muhammad Rafiq A. F. Aljohani Zafar Iqbal Nauman Ahmed Shafiullah Niazai Ilyas Khan |
| author_sort | Mudassar Rafique |
| collection | DOAJ |
| description | Abstract This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in place of integer order derivatives and including the delay factors in the susceptible and infectious compartments. Moreover, unique existence of the solution for the underlying model is ensured by establishing some benchmark results. Likewise, the positivity and boundedness of the solutions for the projected model is explored. The basic reproduction number is $${R}_{0}$$ is found out for the model. The time-delayed non-integer order STID model holds two steady states, namely, the STID free and endemic steady state. The model stability is carried out at the steady states. The non-standard finite difference (NSFD) technique is hybridized with the Grunwald Letnikov (GL) approximation for finding the numerical solutions of the time-delayed non-integer order STID model. The boundedness and non-negativity of the numerical scheme is confirmed. The simulated graphs are presented with the help of an appropriate test example. These graphs show that the proposed numerical algorithm provides the positive bounded solutions. The article is ended with productive outcomes of the study. |
| format | Article |
| id | doaj-art-a7d2527cb7ff49d8b2bbeef1c81cd856 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-a7d2527cb7ff49d8b2bbeef1c81cd8562025-02-02T12:21:58ZengNature PortfolioScientific Reports2045-23222025-01-0115111510.1038/s41598-025-87385-xA new epidemic model of sexually transmittable diseases: a fractional numerical approachMudassar Rafique0Muhammad Aziz Ur Rehamn1Aisha M. Alqahtani2Muhammad Rafiq3A. F. Aljohani4Zafar Iqbal5Nauman Ahmed6Shafiullah Niazai7Ilyas Khan8Department of Mathematics, University of Management and TechnologyDepartment of Mathematics, University of Management and TechnologyDepartment of Mathematical Sciences, College of Science, Princess Nourah Bint Abdulrahman UniversityDepartment of Mathematics, Faculty of Science and Technology, University of Central PunjabDepartment of Mathematics, Faculty of Science, University of TabukDepartment of Mathematics and Statistics, The University of LahoreDepartment of Mathematics, Faculty of Science and Technology, University of Central PunjabDepartment of Mathematics, Education Faculty, Laghman UniversityDepartment of Mathematics, College of Science Al-Zulfi, Majmaah UniversityAbstract This study aims at investigating the dynamics of sexually transmitted infectious disease (STID), which is serious health concern. In so doing, the integer order STID model is progressed in to the time-delayed non-integer order STID model by introducing the Caputo fractional derivatives in place of integer order derivatives and including the delay factors in the susceptible and infectious compartments. Moreover, unique existence of the solution for the underlying model is ensured by establishing some benchmark results. Likewise, the positivity and boundedness of the solutions for the projected model is explored. The basic reproduction number is $${R}_{0}$$ is found out for the model. The time-delayed non-integer order STID model holds two steady states, namely, the STID free and endemic steady state. The model stability is carried out at the steady states. The non-standard finite difference (NSFD) technique is hybridized with the Grunwald Letnikov (GL) approximation for finding the numerical solutions of the time-delayed non-integer order STID model. The boundedness and non-negativity of the numerical scheme is confirmed. The simulated graphs are presented with the help of an appropriate test example. These graphs show that the proposed numerical algorithm provides the positive bounded solutions. The article is ended with productive outcomes of the study.https://doi.org/10.1038/s41598-025-87385-xNew epidemic modelDelayed fractional differential equationsSTIDsVoltera Lyapunov functionLaSalle principalGL non-standard finite difference schemes |
| spellingShingle | Mudassar Rafique Muhammad Aziz Ur Rehamn Aisha M. Alqahtani Muhammad Rafiq A. F. Aljohani Zafar Iqbal Nauman Ahmed Shafiullah Niazai Ilyas Khan A new epidemic model of sexually transmittable diseases: a fractional numerical approach Scientific Reports New epidemic model Delayed fractional differential equations STIDs Voltera Lyapunov function LaSalle principal GL non-standard finite difference schemes |
| title | A new epidemic model of sexually transmittable diseases: a fractional numerical approach |
| title_full | A new epidemic model of sexually transmittable diseases: a fractional numerical approach |
| title_fullStr | A new epidemic model of sexually transmittable diseases: a fractional numerical approach |
| title_full_unstemmed | A new epidemic model of sexually transmittable diseases: a fractional numerical approach |
| title_short | A new epidemic model of sexually transmittable diseases: a fractional numerical approach |
| title_sort | new epidemic model of sexually transmittable diseases a fractional numerical approach |
| topic | New epidemic model Delayed fractional differential equations STIDs Voltera Lyapunov function LaSalle principal GL non-standard finite difference schemes |
| url | https://doi.org/10.1038/s41598-025-87385-x |
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