Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence
This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regener...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2024241?viewType=HTML |
| _version_ | 1797322580104839168 |
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| author | Rongrong Yin Ahmadjan Muhammadhaji |
| author_facet | Rongrong Yin Ahmadjan Muhammadhaji |
| author_sort | Rongrong Yin |
| collection | DOAJ |
| description | This paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results. |
| first_indexed | 2024-03-08T05:15:24Z |
| format | Article |
| id | doaj.art-bab71b35796a415498d275aa1493b076 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-08T05:15:24Z |
| publishDate | 2024-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bab71b35796a415498d275aa1493b0762024-02-07T01:21:48ZengAIMS PressAIMS Mathematics2473-69882024-01-01924962498910.3934/math.2024241Dynamics in a delayed rumor propagation model with logistic growth and saturation incidenceRongrong Yin 0Ahmadjan Muhammadhaji11. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China 2. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, China1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830017, China 2. The Key Laboratory of Applied Mathematics of Xinjiang Uygur Autonomous Region, Xinjiang University, Urumqi 830017, ChinaThis paper studies a delayed rumor propagation model with logistic growth and saturation incidence. The next generation matrix method, some inequality techniques, the Lyapunov-LaSalle invariance principle, and the Lyapunov method are used in this paper. Our results indicate that if the basic regeneration number (which is analogous to the basic reproduction number in disease transmission models) is less than 1, the rumor-free equilibrium point (which is analogous to the disease-free equilibrium point in disease transmission models) is globally stable. If the basic regeneration number is greater than 1, then the rumor is permanent, and some sufficient conditions are obtained for local and global asymptotic stability of the rumor prevailing equilibrium point (which is analogous to the endemic equilibrium point in disease transmission models). Finally, three examples with numerical simulations are presented to illustrate the obtained theoretical results.https://www.aimspress.com/article/doi/10.3934/math.2024241?viewType=HTMLlyapunov-lasalle invariance principlepermanencelyapunov functionalglobal stability |
| spellingShingle | Rongrong Yin Ahmadjan Muhammadhaji Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence AIMS Mathematics lyapunov-lasalle invariance principle permanence lyapunov functional global stability |
| title | Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| title_full | Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| title_fullStr | Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| title_full_unstemmed | Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| title_short | Dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| title_sort | dynamics in a delayed rumor propagation model with logistic growth and saturation incidence |
| topic | lyapunov-lasalle invariance principle permanence lyapunov functional global stability |
| url | https://www.aimspress.com/article/doi/10.3934/math.2024241?viewType=HTML |
| work_keys_str_mv | AT rongrongyin dynamicsinadelayedrumorpropagationmodelwithlogisticgrowthandsaturationincidence AT ahmadjanmuhammadhaji dynamicsinadelayedrumorpropagationmodelwithlogisticgrowthandsaturationincidence |