Stability and computational analysis of Influenza-A epidemic model through double time delay
Delay factors demonstration has a significant role in controlling a strain of infectious disease instead of a pharmaceutical strategy. According to the World Health Organization (WHO), 3–5 million cases are reported annually and approximately 290,000 to 650,000 respiratory deaths annually. So, in th...
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Elsevier
2025-01-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1110016824011128 |
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| author | Ateq Alsaadi Ali Raza Muhammed Bilal Riaz Umar Shafique |
| author_facet | Ateq Alsaadi Ali Raza Muhammed Bilal Riaz Umar Shafique |
| author_sort | Ateq Alsaadi |
| collection | DOAJ |
| description | Delay factors demonstration has a significant role in controlling a strain of infectious disease instead of a pharmaceutical strategy. According to the World Health Organization (WHO), 3–5 million cases are reported annually and approximately 290,000 to 650,000 respiratory deaths annually. So, in the present study, we develop a delayed mathematical model based on delay differential equations (DDEs) for the influenza epidemic using a deterministic approach by introducing double delay parameters. The four distinct sub-populations are considered susceptible, exposed, infected, and recovered. For the rigorous analysis, the fundamental properties of the model like positivity, boundedness, existence, and uniqueness, were studied. The influenza-free equilibrium (IFE) and influenza-existing equilibrium (IEE), are the two nonnegative equilibrium points that the model demonstrates. Both locally and globally, the asymptotic stability of the equilibrium points of the model is established and shown under specific situations of reproduction number. Additionally, investigated the model's parameter sensitivity and determined the relative sensitivity of each parameter. Both standard and nonstandard methods—such as Euler, Runge-Kutta, and nonstandard finite difference with a delayed sense—are presented to make computational analysis support a dynamical analysis and the best visualization of results. The stability of the non-standard finite difference scheme is thoroughly analyzed around the steady states of the model. Additionally, the results show that the nonstandard finite difference approximation is an efficient, cost-effective method, independent of time step size, to solve such highly nonlinear and complex real-world problems. |
| format | Article |
| id | doaj-art-10ee88898e5f44609d760407bf4088fa |
| institution | Kabale University |
| issn | 1110-0168 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj-art-10ee88898e5f44609d760407bf4088fa2025-01-09T06:13:17ZengElsevierAlexandria Engineering Journal1110-01682025-01-011106476Stability and computational analysis of Influenza-A epidemic model through double time delayAteq Alsaadi0Ali Raza1Muhammed Bilal Riaz2Umar Shafique3Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaDepartment of Physical Sciences, The University of Chenab, Gujrat, Pakistan; Corresponding authors.IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czech Republic; Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon; corresponding author at: IT4Innovations, VSB – Technical University of Ostrava, Ostrava, Czech Republic.Department of Mathematics, National College of Business Administration and Economics Lahore, Pakistan; Corresponding authors.Delay factors demonstration has a significant role in controlling a strain of infectious disease instead of a pharmaceutical strategy. According to the World Health Organization (WHO), 3–5 million cases are reported annually and approximately 290,000 to 650,000 respiratory deaths annually. So, in the present study, we develop a delayed mathematical model based on delay differential equations (DDEs) for the influenza epidemic using a deterministic approach by introducing double delay parameters. The four distinct sub-populations are considered susceptible, exposed, infected, and recovered. For the rigorous analysis, the fundamental properties of the model like positivity, boundedness, existence, and uniqueness, were studied. The influenza-free equilibrium (IFE) and influenza-existing equilibrium (IEE), are the two nonnegative equilibrium points that the model demonstrates. Both locally and globally, the asymptotic stability of the equilibrium points of the model is established and shown under specific situations of reproduction number. Additionally, investigated the model's parameter sensitivity and determined the relative sensitivity of each parameter. Both standard and nonstandard methods—such as Euler, Runge-Kutta, and nonstandard finite difference with a delayed sense—are presented to make computational analysis support a dynamical analysis and the best visualization of results. The stability of the non-standard finite difference scheme is thoroughly analyzed around the steady states of the model. Additionally, the results show that the nonstandard finite difference approximation is an efficient, cost-effective method, independent of time step size, to solve such highly nonlinear and complex real-world problems.http://www.sciencedirect.com/science/article/pii/S1110016824011128Novel Influenza SEIR modelDelay differential equations (DDEs)Feasible propertiesStability resultsComputational methodsConvergence analysis |
| spellingShingle | Ateq Alsaadi Ali Raza Muhammed Bilal Riaz Umar Shafique Stability and computational analysis of Influenza-A epidemic model through double time delay Alexandria Engineering Journal Novel Influenza SEIR model Delay differential equations (DDEs) Feasible properties Stability results Computational methods Convergence analysis |
| title | Stability and computational analysis of Influenza-A epidemic model through double time delay |
| title_full | Stability and computational analysis of Influenza-A epidemic model through double time delay |
| title_fullStr | Stability and computational analysis of Influenza-A epidemic model through double time delay |
| title_full_unstemmed | Stability and computational analysis of Influenza-A epidemic model through double time delay |
| title_short | Stability and computational analysis of Influenza-A epidemic model through double time delay |
| title_sort | stability and computational analysis of influenza a epidemic model through double time delay |
| topic | Novel Influenza SEIR model Delay differential equations (DDEs) Feasible properties Stability results Computational methods Convergence analysis |
| url | http://www.sciencedirect.com/science/article/pii/S1110016824011128 |
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