Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects
In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive inv...
| Main Authors: | , , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-04-01
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| Series: | Alexandria Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S111001682300042X |
| _version_ | 1797847699456786432 |
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| author | Saima Rashid Ahmed A. El-Deeb Mustafa Inc Ali Akgül Mohammed Zakarya Wajaree Weera |
| author_facet | Saima Rashid Ahmed A. El-Deeb Mustafa Inc Ali Akgül Mohammed Zakarya Wajaree Weera |
| author_sort | Saima Rashid |
| collection | DOAJ |
| description | In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive R0s as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients. |
| first_indexed | 2024-04-09T18:16:37Z |
| format | Article |
| id | doaj.art-68ec573dde5f48c1a2e34aab5c102c05 |
| institution | Directory Open Access Journal |
| issn | 1110-0168 |
| language | English |
| last_indexed | 2024-04-09T18:16:37Z |
| publishDate | 2023-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Alexandria Engineering Journal |
| spelling | doaj.art-68ec573dde5f48c1a2e34aab5c102c052023-04-13T04:26:13ZengElsevierAlexandria Engineering Journal1110-01682023-04-01693555Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effectsSaima Rashid0Ahmed A. El-Deeb1Mustafa Inc2Ali Akgül3Mohammed Zakarya4Wajaree Weera5Department of Mathematics, Government College University, Faisalabad 38000, Pakistan; Corresponding authors at: Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkiye (M. Inc).Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Cairo, EgyptDepartment of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkiye; Department of Medical Research, China Medical University, 40402 Taichung, Taiwan; Corresponding authors at: Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkiye (M. Inc).Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia/Mersin 10, TurkeyDepartment of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand; Corresponding authors at: Department of Mathematics, Science Faculty, Firat University, 23119 Elazig, Turkiye (M. Inc).In this paper, we suggest and assess a stochastic model for pneumonia-typhoid co-infection to investigate their distinctive correlation under the impact of preventative techniques considering environmental noise and piecewise fractional derivative operators. Initially, we conducted a descriptive investigation of the model, and the basic reproductive number is defined in terms of the existence and stability of dynamic equilibrium. Then, we obtain the sufficient requirements for the existence of an ergodic stationary distribution by utilizing a novel methodology for constructing stochastic Lyapunov candidates. Besides that, the basic stochastic reproductive R0s as a threshold that will examine the extinction and persistence of the disease. Through a rigorous analysis, this study presents the concept of piecewise derivative with the goal of modelling the co-dynamics of pneumonia and typhoid fever with varying kernels. We viewed various possibilities and described numerical strategies for addressing difficulties. Visual observations, such as chaotic and dynamical behaviour patterns, are provided to demonstrate the efficacy of the proposed notion. Thus, the innovative considerations of fractional calculus include more versatile configurations, allowing us to more effectively acclimate to the dynamic system behaviours of real-world manifestations. Finally, we discovered that treating pneumonia with typhoid fever preventative measures is the least expensive. As a result, for advantageous and cost-effective regulation of both pathogens, legislators must prioritize preventative measures while not overlooking treatment of affected patients.http://www.sciencedirect.com/science/article/pii/S111001682300042XCo-dynamic of pneumonia and typhoid modelFractional derivativesStochastic-deterministic modelsNumerical solutionsItô derivativeChaotic attractors |
| spellingShingle | Saima Rashid Ahmed A. El-Deeb Mustafa Inc Ali Akgül Mohammed Zakarya Wajaree Weera Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects Alexandria Engineering Journal Co-dynamic of pneumonia and typhoid model Fractional derivatives Stochastic-deterministic models Numerical solutions Itô derivative Chaotic attractors |
| title | Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects |
| title_full | Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects |
| title_fullStr | Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects |
| title_full_unstemmed | Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects |
| title_short | Stochastic dynamical analysis of the co-infection of the fractional pneumonia and typhoid fever disease model with cost-effective techniques and crossover effects |
| title_sort | stochastic dynamical analysis of the co infection of the fractional pneumonia and typhoid fever disease model with cost effective techniques and crossover effects |
| topic | Co-dynamic of pneumonia and typhoid model Fractional derivatives Stochastic-deterministic models Numerical solutions Itô derivative Chaotic attractors |
| url | http://www.sciencedirect.com/science/article/pii/S111001682300042X |
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