Analysis of a SIR model with pulse vaccination and temporary immunity: Stability, bifurcation and a cylindrical attractor
| Autor: | Xinzhi Liu, Kevin E. M. Church |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Discretization
Applied Mathematics 010102 general mathematics Mathematical analysis General Engineering General Medicine Quantitative Biology::Other 01 natural sciences 3. Good health 010101 applied mathematics Computational Mathematics Transcritical bifurcation Numerical continuation Attractor Quantitative Biology::Populations and Evolution Cylinder Artificial induction of immunity 0101 mathematics Invariant (mathematics) General Economics Econometrics and Finance Analysis Bifurcation Mathematics |
| Zdroj: | Nonlinear Analysis: Real World Applications. 50:240-266 |
| ISSN: | 1468-1218 |
| DOI: | 10.1016/j.nonrwa.2019.04.015 |
| Popis: | A time-delayed SIR model with general nonlinear incidence rate, pulse vaccination and temporary immunity is developed. The basic reproduction number is derived and it is shown that the disease-free periodic solution generically undergoes a transcritical bifurcation to an endemic periodic solution as the vaccination coverage drops below a critical level. Using numerical continuation and a monodromy operator discretization scheme, we track the bifurcating endemic periodic solution as the vaccination coverage is decreased and a Hopf point is detected. This leads to a bifurcation to an attracting, invariant cylinder. As the vaccination coverage is further decreased, the geometry of the cylinder contracts along its length until it finally collapses to a periodic orbit when the vaccination coverage goes to zero. In the intermediate regime, phase locking on the cylinder is observed. |
| Databáze: | OpenAIRE |
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