Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator
In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2024/2580745 |
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| _version_ | 1841524309166653440 |
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| author | Bushra Bajjah Mahmut Modanli |
| author_facet | Bushra Bajjah Mahmut Modanli |
| author_sort | Bushra Bajjah |
| collection | DOAJ |
| description | In this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number Rp°. The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if Rp°<1, then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst Rp°>1, the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab. |
| format | Article |
| id | doaj-art-dfcea414db0142e9b91f32c8201a592d |
| institution | Kabale University |
| issn | 1607-887X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-dfcea414db0142e9b91f32c8201a592d2025-02-03T07:23:23ZengWileyDiscrete Dynamics in Nature and Society1607-887X2024-01-01202410.1155/2024/2580745Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo OperatorBushra Bajjah0Mahmut Modanli1Thamar UniversityHarran UniversityIn this paper, a fractional model in the Caputo sense is used to characterize the dynamics of HPV with cervical cancer. Generalized mean value theorem has been used to examine whether the infection model has a unique positive solution. The model has two equilibrium points: the disease-free point and the endemic point. The examination of the system’s local and global stability is provided in terms of the basic reproductive number Rp°. The global stability analysis has been carried out using an appropriate Lyapunov function and the LaSalle invariant principle. The results demonstrate that in the infection model, if Rp°<1, then the solution converges to the disease-free equilibrium, which is both locally and globally asymptotically stable. Whilst Rp°>1, the endemic equilibrium is considered to exist. Simulations are implemented via a finite difference method with Grünwald-Letnikov discretization approach for Caputo derivative operator to define how changes in parameters impact the dynamic behavior of the system using Matlab.http://dx.doi.org/10.1155/2024/2580745 |
| spellingShingle | Bushra Bajjah Mahmut Modanli Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator Discrete Dynamics in Nature and Society |
| title | Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator |
| title_full | Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator |
| title_fullStr | Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator |
| title_full_unstemmed | Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator |
| title_short | Finite Difference Method for Infection Model of HPV with Cervical Cancer under Caputo Operator |
| title_sort | finite difference method for infection model of hpv with cervical cancer under caputo operator |
| url | http://dx.doi.org/10.1155/2024/2580745 |
| work_keys_str_mv | AT bushrabajjah finitedifferencemethodforinfectionmodelofhpvwithcervicalcancerundercaputooperator AT mahmutmodanli finitedifferencemethodforinfectionmodelofhpvwithcervicalcancerundercaputooperator |