Epidemic outbreaks in structured host populations
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916710421889024 |
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| author | Thieme, Horst R |
| author_facet | Thieme, Horst R |
| contents | For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are typically established by imposing conditions that make $\cR_0$ an eigenvalue of the NGO associated with a positive eigenvector and a positive eigenfunctional (eigenvector of the dual of the NGO). More general results can be obtained by imposing conditions that associate $\cR_0$ just with a positive eigenfunctional. The next generation operator is conveniently expressed by a measure kernel or a Feller kernel which enables the use of analytic rather than functional analytic methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_09778 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Epidemic outbreaks in structured host populations Thieme, Horst R Populations and Evolution Analysis of PDEs 92D30, 92D25, 28A25, 45H05, 45M99, 47J05, 47N20 For a heterogeneous host population, the basic reproduction number of an infectious disease, $\cR_0$, is defined as the spectral radius of the next generation operator (NGO). The threshold properties of the basic reproduction number are typically established by imposing conditions that make $\cR_0$ an eigenvalue of the NGO associated with a positive eigenvector and a positive eigenfunctional (eigenvector of the dual of the NGO). More general results can be obtained by imposing conditions that associate $\cR_0$ just with a positive eigenfunctional. The next generation operator is conveniently expressed by a measure kernel or a Feller kernel which enables the use of analytic rather than functional analytic methods. |
| title | Epidemic outbreaks in structured host populations |
| topic | Populations and Evolution Analysis of PDEs 92D30, 92D25, 28A25, 45H05, 45M99, 47J05, 47N20 |
| url | https://arxiv.org/abs/2411.09778 |