{"paper":{"title":"Weak Convergence of a Seasonally Forced Stochastic Epidemic Model","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alun Lloyd, Yuan Zhang","submitted_at":"2014-12-02T16:26:14Z","abstract_excerpt":"In this study we extend the results of Kurtz (1970,1971) to show the weak convergence of epidemic processes that include explicit time dependence, specifically where the transmission parameter,$\\beta(t)$, carries a time dependency. We first show that when population size goes to infinity, the time inhomogeneous process converges weakly to the solution of the mean-field ODE. Our second result is that, under proper scaling, the central limit type fluctuations converge to a diffusion process."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.0964","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"}