Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models
Abstract Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided f...
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Nature Portfolio
2025-01-01
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| Online Access: | https://doi.org/10.1038/s41598-024-80166-y |
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| author | Divine Wanduku Md Mahmud Hasan |
| author_facet | Divine Wanduku Md Mahmud Hasan |
| author_sort | Divine Wanduku |
| collection | DOAJ |
| description | Abstract Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control. The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. Key statistical properties and the basic reproduction number ( $$\mathfrak{R}_{0}$$ ) are derived, and conditions for the system’s asymptotic autonomy are established for specific lifetime distributions. Four HRF behaviors—monotonic, bathtub, reverse bathtub, and constant—are analyzed to determine conditions for disease eradication and the asymptotic population under these scenarios. Sensitivity analysis examines how HRF behaviors shape system trajectories. Numerical simulations illustrate the influence of diverse lifetime models on vaccine efficacy and immunity, offering insights for effective disease management. |
| format | Article |
| id | doaj-art-779ddb05bb3f4ce78b280cfb1a88af00 |
| institution | Kabale University |
| issn | 2045-2322 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Nature Portfolio |
| record_format | Article |
| series | Scientific Reports |
| spelling | doaj-art-779ddb05bb3f4ce78b280cfb1a88af002025-01-19T12:24:29ZengNature PortfolioScientific Reports2045-23222025-01-0115113910.1038/s41598-024-80166-yCompartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic ModelsDivine Wanduku0Md Mahmud Hasan1Department of Mathematical Sciences, Georgia Southern UniversityDepartment of Biostatistics, Data Science and Epidemiology, School of Public Health, Augusta UniversityAbstract Compartmental models with exponentially distributed lifetime stages assume a constant hazard rate, limiting their scope. This study develops a theoretical framework for systems with general lifetime distributions, modeled as transition rates in a renewal process. Applications are provided for the SVIS (Susceptible-Vaccinated-Infected-Susceptible) disease epidemic model to investigate the impacts of hazard rate functions (HRFs) on disease control. The novel SVIS model is formulated as a non-autonomous nonlinear system (NANLS) of ordinary differential equations (ODEs), with coefficients defined by HRFs. Key statistical properties and the basic reproduction number ( $$\mathfrak{R}_{0}$$ ) are derived, and conditions for the system’s asymptotic autonomy are established for specific lifetime distributions. Four HRF behaviors—monotonic, bathtub, reverse bathtub, and constant—are analyzed to determine conditions for disease eradication and the asymptotic population under these scenarios. Sensitivity analysis examines how HRF behaviors shape system trajectories. Numerical simulations illustrate the influence of diverse lifetime models on vaccine efficacy and immunity, offering insights for effective disease management. https://doi.org/10.1038/s41598-024-80166-yHazard rate functionJump ProcessNon-autonomous ODERenewal processAsymptotically autonomous systemSVIS model |
| spellingShingle | Divine Wanduku Md Mahmud Hasan Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models Scientific Reports Hazard rate function Jump Process Non-autonomous ODE Renewal process Asymptotically autonomous system SVIS model |
| title | Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models |
| title_full | Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models |
| title_fullStr | Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models |
| title_full_unstemmed | Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models |
| title_short | Compartmental Models Driven by Renewal Processes: Survival Analysis and Applications to SVIS Epidemic Models |
| title_sort | compartmental models driven by renewal processes survival analysis and applications to svis epidemic models |
| topic | Hazard rate function Jump Process Non-autonomous ODE Renewal process Asymptotically autonomous system SVIS model |
| url | https://doi.org/10.1038/s41598-024-80166-y |
| work_keys_str_mv | AT divinewanduku compartmentalmodelsdrivenbyrenewalprocessessurvivalanalysisandapplicationstosvisepidemicmodels AT mdmahmudhasan compartmentalmodelsdrivenbyrenewalprocessessurvivalanalysisandapplicationstosvisepidemicmodels |