Asymptotic solutions of the SIR and SEIR models well above the epidemic threshold

Abstract

A simple and explicit expression of the solution of the SIR epidemiological model of Kermack and McKendrick is constructed in the asymptotic limit of large basic reproduction numbers $\ro$. The proposed formula yields good qualitative agreement already when $\ro\geq3$ and rapidly becomes quantitatively accurate as larger values of $\ro$ are assumed. The derivation is based on the method of matched asymptotic expansions, which exploits the fact that the exponential growing phase and the eventual recession of the outbreak occur on distinct time scales. From the newly derived solution, an analytical estimate of the time separating the first inflexion point of the epidemic curve from the peak of infections is given.

Research and Practice Analysis of Higher Vocational Colleges Facing the Experience and Dissemination of Regional Characteristic Tea Culture

“…Although scholars at home and abroad have carried out more research on blockchain technology, the field of network public opinion mainly focuses on the theoretical research and application level, and has not formed a systematic system [8]. erefore, the information dissemination model based on blockchain technology is still in the development stage, and will be studied gradually in the future [9].…”

Logistic growth on networks: exact solutions for the SI model

“…Typically, there are two approaches to formulate spreading processes: a collective approach based on deterministic compartmental models governing the state of the population as a whole [1,[11][12][13] and a more detailed approach aimed at describing the stochastic individual interactions [14][15][16]. Various approximation and numerical schemes have been used to solve compartmental models of epidemic spreading, and in certain cases, exact results are known [17][18][19][20]. These models are effective and often give a good estimate of the temporal evolution of the system.…”