Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model
Abstract As the fear of infection is a crucial factor in the progress of the disease in the population. We aim, in this study, to investigate a susceptible-protected-infected-recovered (SPIR) epidemic model with mixed diffusion modeled by local and nonlocal diffusions. These types of diffusion are u...
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Nature Portfolio
2025-08-01
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| Series: | Scientific Reports |
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| Online Access: | https://doi.org/10.1038/s41598-025-16280-2 |
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| author | Ghilmana Sarmad Salih Djilali Soufiane Bentout Abdessamad Tridane |
| author_facet | Ghilmana Sarmad Salih Djilali Soufiane Bentout Abdessamad Tridane |
| author_sort | Ghilmana Sarmad |
| collection | DOAJ |
| description | Abstract As the fear of infection is a crucial factor in the progress of the disease in the population. We aim, in this study, to investigate a susceptible-protected-infected-recovered (SPIR) epidemic model with mixed diffusion modeled by local and nonlocal diffusions. These types of diffusion are used to model the fear effect of being infected by the population. The model is shown to be well-posed; the solution exists, is positive, and is unique. The variational expression is obtained to determine threshold role of $$\mathfrak {R}_0$$ , also known as the basic reproduction number. Indeed, for $$\mathfrak {R}_0<1$$ , we show that the epidemic will extinct, corresponding to the global asymptotic stability of the infection-free equilibrium state. However, when $$\mathfrak {R}_0>1$$ , the existence of the infection equilibrium state and the uniform persistence of the solution have been proved. The Lyapunov function have been used to show the global asymptotic stability of the infection equilibrium state. Moreover, we compared the obtained results with the classical SIR epidemic model for determining the required protection function for stopping the disease, which can be obtained by reducing $$\mathfrak {R}_0$$ below one. |
| format | Article |
| id | doaj-art-6df675d86e0b4e21844e4c94e2c09dc7 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | Nature Portfolio |
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| series | Scientific Reports |
| spelling | doaj-art-6df675d86e0b4e21844e4c94e2c09dc72025-08-24T11:26:53ZengNature PortfolioScientific Reports2045-23222025-08-0115112710.1038/s41598-025-16280-2Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic modelGhilmana Sarmad0Salih Djilali1Soufiane Bentout2Abdessamad Tridane3Department of Mathematical Sciences, United Arab Emirates UniversityDepartment of Mathematics, Faculty of Exact Sciences and Informatics, Hassiba Benbouali UniversityDepartment of Mathematics and Informatics, University Ain Temouchent, Belhadj BouchaibDepartment of Mathematical Sciences, United Arab Emirates UniversityAbstract As the fear of infection is a crucial factor in the progress of the disease in the population. We aim, in this study, to investigate a susceptible-protected-infected-recovered (SPIR) epidemic model with mixed diffusion modeled by local and nonlocal diffusions. These types of diffusion are used to model the fear effect of being infected by the population. The model is shown to be well-posed; the solution exists, is positive, and is unique. The variational expression is obtained to determine threshold role of $$\mathfrak {R}_0$$ , also known as the basic reproduction number. Indeed, for $$\mathfrak {R}_0<1$$ , we show that the epidemic will extinct, corresponding to the global asymptotic stability of the infection-free equilibrium state. However, when $$\mathfrak {R}_0>1$$ , the existence of the infection equilibrium state and the uniform persistence of the solution have been proved. The Lyapunov function have been used to show the global asymptotic stability of the infection equilibrium state. Moreover, we compared the obtained results with the classical SIR epidemic model for determining the required protection function for stopping the disease, which can be obtained by reducing $$\mathfrak {R}_0$$ below one.https://doi.org/10.1038/s41598-025-16280-2Delayed epidemic modelDiffusionNonlocal diffusionprotectionFear effect |
| spellingShingle | Ghilmana Sarmad Salih Djilali Soufiane Bentout Abdessamad Tridane Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model Scientific Reports Delayed epidemic model Diffusion Nonlocal diffusion protection Fear effect |
| title | Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model |
| title_full | Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model |
| title_fullStr | Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model |
| title_full_unstemmed | Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model |
| title_short | Fear effect on the mobility of individuals in a spatially heterogeneous environment: a delayed diffusive SPIR epidemic model |
| title_sort | fear effect on the mobility of individuals in a spatially heterogeneous environment a delayed diffusive spir epidemic model |
| topic | Delayed epidemic model Diffusion Nonlocal diffusion protection Fear effect |
| url | https://doi.org/10.1038/s41598-025-16280-2 |
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