Stability Analysis and Simulation of Diffusive Vaccinated Models
This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously e...
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| Main Authors: | , , , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2024/5595996 |
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| author | Mohammed M. Al-Shamiri N. Avinash P. Chellamani Manal Z. M. Abdallah G. Britto Antony Xavier V. Rexma Sherine M. Abisha |
| author_facet | Mohammed M. Al-Shamiri N. Avinash P. Chellamani Manal Z. M. Abdallah G. Britto Antony Xavier V. Rexma Sherine M. Abisha |
| author_sort | Mohammed M. Al-Shamiri |
| collection | DOAJ |
| description | This paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease’s time transmission, it is important to examine the global stability of the equilibrium points. Disease-free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease-free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler’s approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission. |
| format | Article |
| id | doaj-art-52499f08f3db474bb469dcbb9391762a |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-52499f08f3db474bb469dcbb9391762a2025-02-03T11:28:18ZengWileyComplexity1099-05262024-01-01202410.1155/2024/5595996Stability Analysis and Simulation of Diffusive Vaccinated ModelsMohammed M. Al-Shamiri0N. Avinash1P. Chellamani2Manal Z. M. Abdallah3G. Britto Antony Xavier4V. Rexma Sherine5M. Abisha6Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsThis paper begins by analyzing the key mathematical properties of diffusive vaccinated models, including existence, uniqueness, positivity, and boundedness. Equilibria are identified, and the basic reproductive number is calculated. The Banach contraction mapping principle is applied to rigorously establish the solution existence and uniqueness. In order to understand the disease’s time transmission, it is important to examine the global stability of the equilibrium points. Disease-free equilibrium and endemic equilibrium are the two equilibria in this model. Here, we demonstrate that the endemic equilibrium is worldwide asymptotic stable when the basic reproductive number is greater than 1, and the disease-free equilibrium is globally asymptotic stable whenever the basic reproductive number is less than 1. Moreover, based on the Caputo fractional derivative of order and the implicit Euler’s approximation, we offered an unconditionally stable numerical solution for the resultant system. This work explores the solution of some significant population models of noninteger order using an approach known as the iterative Laplace transform. The proposed methodology is developed by effectively combining Laplace transformation with an iterative procedure. A series form solution that exhibits some convergent behavior towards the precise solution can be attained. It is noted that there is a close contact between the obtained and precise solutions. Moreover, the suggested method can handle a variety of fractional order derivative problems because it involves minimal computations. This information will be helpful in further studies to determine the ideal strategy of action for preventing or stopping the spread disease transmission.http://dx.doi.org/10.1155/2024/5595996 |
| spellingShingle | Mohammed M. Al-Shamiri N. Avinash P. Chellamani Manal Z. M. Abdallah G. Britto Antony Xavier V. Rexma Sherine M. Abisha Stability Analysis and Simulation of Diffusive Vaccinated Models Complexity |
| title | Stability Analysis and Simulation of Diffusive Vaccinated Models |
| title_full | Stability Analysis and Simulation of Diffusive Vaccinated Models |
| title_fullStr | Stability Analysis and Simulation of Diffusive Vaccinated Models |
| title_full_unstemmed | Stability Analysis and Simulation of Diffusive Vaccinated Models |
| title_short | Stability Analysis and Simulation of Diffusive Vaccinated Models |
| title_sort | stability analysis and simulation of diffusive vaccinated models |
| url | http://dx.doi.org/10.1155/2024/5595996 |
| work_keys_str_mv | AT mohammedmalshamiri stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT navinash stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT pchellamani stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT manalzmabdallah stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT gbrittoantonyxavier stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT vrexmasherine stabilityanalysisandsimulationofdiffusivevaccinatedmodels AT mabisha stabilityanalysisandsimulationofdiffusivevaccinatedmodels |