khaoot, R. (2024) A discrete-time mathematical model including vaccination for the spread of infectious diseases with a saturated nonlinear spread rate. Masters thesis, University of Zabol.
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A discrete-time mathematical model including vaccination for the spread of infectious diseases with a saturated nonlinear spread rate.pdf Download (333kB) |
Abstract
This research presents a compelling discrete-time SIS (Susceptible-Infected-Susceptible) epidemic model that effectively integrates a vaccination program. Our model accounts for both natural mortality and deaths caused by the disease, while allowing for a dynamic total population. We meticulously describe the model’s components and parameters, detailing how individuals transition between various states. This leads us to derive crucial equilibrium points, including the disease-free equilibrium and the endemic equilibrium. Importantly, we introduce a general generating function that serves as the key determinant of community behavior through a specific threshold value. By employing suitable Lyapunov functions, we articulate the model's global dynamics. When this threshold is less than or equal to one, the disease-free equilibrium achieves global asymptotic stability, demonstrating that eradication is possible. Conversely, exceeding this threshold indicates global asymptotic stability for the endemic equilibrium, revealing that the disease will remain a persistent threat. Additionally, we thoroughly examine significant model bifurcations, including fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation. Our numerical simulations robustly support the theoretical findings, offering valuable insights through bifurcation diagrams, Lyapunov exponents, and detailed model solutions. This research not only enhances our understanding of epidemic dynamics but also informs effective public health strategies.
| Item Type: | Thesis (Masters) |
|---|---|
| Uncontrolled Keywords: | SIS epidemic model, vaccination, contagion number, bifurcation, Lyapunov view, chaos |
| Subjects: | Q Science > QH Natural history > QH301 Biology |
| Depositing User: | Mrs najmeh khajeh |
| Date Deposited: | 03 May 2025 07:57 |
| Last Modified: | 03 May 2025 07:57 |
| URI: | http://eprints.uoz.ac.ir/id/eprint/3807 |
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