Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay
Impetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (i...
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MDPI AG
2024-11-01
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| author | Yanan Wang Tiansi Zhang |
| author_facet | Yanan Wang Tiansi Zhang |
| author_sort | Yanan Wang |
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| description | Impetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (impetigo) is developed with a specific emphasis on the time delay effects in the infection and recovery processes. To address this complexity, we introduce a delay differential equation (DDE) to describe the dynamic process. We analyzed the existence of Hopf bifurcations associated with the two equilibrium points and examined the mechanisms underlying the occurrence of these bifurcations as delays exceeded certain critical values. To obtain more comprehensive insights into this phenomenon, we applied the center manifold theory and the normal form method to determine the direction and stability of Hopf bifurcations near bifurcation curves. This research not only offers a novel theoretical perspective on the transmission of impetigo but also lays a significant mathematical foundation for developing clinical intervention strategies. Specifically, it suggests that an increased time delay between infection and isolation could lead to more severe outbreaks, further supporting the development of more effective intervention approaches. |
| format | Article |
| id | doaj-art-94e636deefc64b398b2d40944d4e6768 |
| institution | OA Journals |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | MDPI AG |
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| series | Axioms |
| spelling | doaj-art-94e636deefc64b398b2d40944d4e67682025-08-20T02:26:59ZengMDPI AGAxioms2075-16802024-11-01131179810.3390/axioms13110798Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time DelayYanan Wang0Tiansi Zhang1College of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaCollege of Science, University of Shanghai for Science and Technology, Shanghai 200093, ChinaImpetigo is a highly contagious skin infection that primarily affects children and communities in low-income regions and has become a significant public health issue impacting both individuals and healthcare systems. A nonlinear deterministic model based on the transmission dynamics of skin sores (impetigo) is developed with a specific emphasis on the time delay effects in the infection and recovery processes. To address this complexity, we introduce a delay differential equation (DDE) to describe the dynamic process. We analyzed the existence of Hopf bifurcations associated with the two equilibrium points and examined the mechanisms underlying the occurrence of these bifurcations as delays exceeded certain critical values. To obtain more comprehensive insights into this phenomenon, we applied the center manifold theory and the normal form method to determine the direction and stability of Hopf bifurcations near bifurcation curves. This research not only offers a novel theoretical perspective on the transmission of impetigo but also lays a significant mathematical foundation for developing clinical intervention strategies. Specifically, it suggests that an increased time delay between infection and isolation could lead to more severe outbreaks, further supporting the development of more effective intervention approaches.https://www.mdpi.com/2075-1680/13/11/798time delaystabilitybifurcating periodic solutionHopf bifurcation |
| spellingShingle | Yanan Wang Tiansi Zhang Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay Axioms time delay stability bifurcating periodic solution Hopf bifurcation |
| title | Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay |
| title_full | Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay |
| title_fullStr | Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay |
| title_full_unstemmed | Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay |
| title_short | Stability and Bifurcation Analysis for the Transmission Dynamics of Skin Sores with Time Delay |
| title_sort | stability and bifurcation analysis for the transmission dynamics of skin sores with time delay |
| topic | time delay stability bifurcating periodic solution Hopf bifurcation |
| url | https://www.mdpi.com/2075-1680/13/11/798 |
| work_keys_str_mv | AT yananwang stabilityandbifurcationanalysisforthetransmissiondynamicsofskinsoreswithtimedelay AT tiansizhang stabilityandbifurcationanalysisforthetransmissiondynamicsofskinsoreswithtimedelay |