Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations
In this work, the application of the system of fractal fractional differential equations is exploited. Infectious diseases modeling of non-integer order attracts many mathematicians and biological scientists. The presentation of an advanced fractal fractional model for studying the exact dynamical b...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003760 |
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| author | Razia Begum Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad |
| author_facet | Razia Begum Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad |
| author_sort | Razia Begum |
| collection | DOAJ |
| description | In this work, the application of the system of fractal fractional differential equations is exploited. Infectious diseases modeling of non-integer order attracts many mathematicians and biological scientists. The presentation of an advanced fractal fractional model for studying the exact dynamical behavior of infectious diseases in epidemiology is necessary. In this study, a new version of a mathematical model for whooping cough is presented. Whooping cough is a disease and can be transmitted from humans to humans through various means, i.e., touch, cough, and air droplets. In this study, we considered the whooping cough model with a new permanent compartment. Our modified model after incorporating the permanent recovered compartment explains better regarding the individuals who have developed long term immunity against whooping cough. This addition to the model enhances the model’s accuracy towards real world scenarios. The considered model was analyzed by using a system of fractal fractional differential equations, and numerical simulation was established for the findings of this study. The fixed point theorem was used to determine the existence, uniqueness, and Hyers–Ulam stability of the model. Numerical results of the dynamical behavior of the model are also recorded in tables. |
| format | Article |
| id | doaj-art-8de7faa5ad9842f0a2789e90727f2ff1 |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-8de7faa5ad9842f0a2789e90727f2ff12024-12-13T11:05:52ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100990Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equationsRazia Begum0Sajjad Ali1Nahid Fatima2Kamal Shah3Thabet Abdeljawad4Department of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, KPK, PakistanDepartment of Mathematics, Shaheed Benazir Bhutto University, Sheringal, Dir Upper, KPK, Pakistan; Corresponding authors.Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi ArabiaDepartment of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia; Department of Mathematics and Applied Mathematics, School of Science and Technology, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South Africa; Center for Applied Mathematics and Bioinformatics (CAMB), Gulf University for Science and Technology, Hawally, 32093, Kuwait; Corresponding authors.In this work, the application of the system of fractal fractional differential equations is exploited. Infectious diseases modeling of non-integer order attracts many mathematicians and biological scientists. The presentation of an advanced fractal fractional model for studying the exact dynamical behavior of infectious diseases in epidemiology is necessary. In this study, a new version of a mathematical model for whooping cough is presented. Whooping cough is a disease and can be transmitted from humans to humans through various means, i.e., touch, cough, and air droplets. In this study, we considered the whooping cough model with a new permanent compartment. Our modified model after incorporating the permanent recovered compartment explains better regarding the individuals who have developed long term immunity against whooping cough. This addition to the model enhances the model’s accuracy towards real world scenarios. The considered model was analyzed by using a system of fractal fractional differential equations, and numerical simulation was established for the findings of this study. The fixed point theorem was used to determine the existence, uniqueness, and Hyers–Ulam stability of the model. Numerical results of the dynamical behavior of the model are also recorded in tables.http://www.sciencedirect.com/science/article/pii/S2666818124003760Fractal fractional derivativesExistenceUniquenessStabilitySimulation |
| spellingShingle | Razia Begum Sajjad Ali Nahid Fatima Kamal Shah Thabet Abdeljawad Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations Partial Differential Equations in Applied Mathematics Fractal fractional derivatives Existence Uniqueness Stability Simulation |
| title | Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations |
| title_full | Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations |
| title_fullStr | Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations |
| title_full_unstemmed | Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations |
| title_short | Dynamical behavior of whooping cough SVEIQRP model via system of fractal fractional differential equations |
| title_sort | dynamical behavior of whooping cough sveiqrp model via system of fractal fractional differential equations |
| topic | Fractal fractional derivatives Existence Uniqueness Stability Simulation |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003760 |
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