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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.02092 |
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| _version_ | 1866911161269616640 |
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| author | Keliger, Dániel |
| author_facet | Keliger, Dániel |
| contents | We are investigating deterministic SIS dynamics on large networks starting from only a few infected individuals. Under mild assumptions we show that any two epidemic curves - on the same network and with the same parameters - are almost identical up to time translation when initial conditions are small enough regardless of how infections are distributed at the beginning. The limit object - an epidemic starting from the infinite past with infinitesimal prevalence - is identified as the nontrivial eternal solution connecting the disease free state with the endemic equilibrium. Our framework covers several benchmark models including the N-Intertwined Mean Field Approximation (NIMFA) and the Inhomogeneous Mean Field Approximation (IMFA). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02092 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Universality of SIS epidemics starting from small initial conditions Keliger, Dániel Analysis of PDEs Physics and Society We are investigating deterministic SIS dynamics on large networks starting from only a few infected individuals. Under mild assumptions we show that any two epidemic curves - on the same network and with the same parameters - are almost identical up to time translation when initial conditions are small enough regardless of how infections are distributed at the beginning. The limit object - an epidemic starting from the infinite past with infinitesimal prevalence - is identified as the nontrivial eternal solution connecting the disease free state with the endemic equilibrium. Our framework covers several benchmark models including the N-Intertwined Mean Field Approximation (NIMFA) and the Inhomogeneous Mean Field Approximation (IMFA). |
| title | Universality of SIS epidemics starting from small initial conditions |
| topic | Analysis of PDEs Physics and Society |
| url | https://arxiv.org/abs/2204.02092 |