{"paper":{"title":"Explosiveness of Age-Dependent Branching Processes with Contagious and Incubation Periods","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Lennart Gulikers","submitted_at":"2015-10-12T09:18:56Z","abstract_excerpt":"We study explosiveness of age-dependent branching processes describing the early stages of an epidemic-spread: both forward- and backward process are analysed. For the classical age-dependent branching process $(h,G)$, where the offspring has probability generating function $h$ and all individuals have life-lengths independently picked from a distribution $G$, we focus on the setting $h = h_{\\alpha}^L$, with $L$ a function varying slowly at infinity and $\\alpha \\in (0,1)$. Here, $h^L_{\\alpha}(s) = 1 - (1-s)^{\\alpha} L(\\frac{1}{1-s}),$ as $s \\to 1$. For a fixed $G$, the process $(h^L_{\\alpha},G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.03193","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}