Near-exact explicit asymptotic solution of the SIR model well above the epidemic threshold

  title={Near-exact explicit asymptotic solution of the SIR model well above the epidemic threshold},
  author={Gregory Kozyreff},
  • G. Kozyreff
  • Published in medRxiv 29 March 2021
  • Mathematics
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 $rogeq3$ 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… 
2 Citations
Logistic growth on networks: exact solutions for the SI model
This work uses a novel formulation inspired by the mathematical treatment of many-body quantum systems to organize the time-dependent expectation values for the state of individual nodes in terms of contributions from subgraphs of the network.
Research and Practice Analysis of Higher Vocational Colleges Facing the Experience and Dissemination of Regional Characteristic Tea Culture
  • X. Yan
  • Computer Science
    Advances in Multimedia
  • 2022
This paper analyzes the development of computer technology in the background of big data, summarizes the necessity of using computerTechnology in the dissemination of tea culture information, and considers the application strategy of computer Technology in the dissemination ofTea culture information from the perspective ofbig data, hoping to enter a more ideal pattern of teaculture information dissemination.


Accurate closed-form solution of the SIR epidemic model
Exact solution to a dynamic SIR model
Analytical solution of the SIR-model for the temporal evolution of epidemics. Part A: time-independent reproduction factor
We revisit the susceptible-infectious-recovered/removed (SIR) model which is one of the simplest compartmental models. Many epidemological models are derivatives of this basic form. While an analytic
The explicit series solution of SIR and SIS epidemic models
An Approximate Analytical Solution to the Sir Model
An analytical expression, a formula, for the removed individuals in an epidemic, as a function of time, is suggested as an approximation of a Susceptible, Infected, Removed (SIR) epiemics dynamics
Kermack-McKendrick epidemic model revisited
This paper proposes a stochastic diffusion model for the spread of a susceptible-infective-removed Kermack–McKendric epidemic (M1) in a population which size is a martingale $N_t$ that solves the
Deterministic and Stochastic Epidemics in Closed Populations
The problem of the growth of a stochastic epidemic in a closed population is a very challenging one; from one point of view it is almost trivial, for we have only to deal with a temporally
A time delay dynamical model for outbreak of 2019-nCoV and the parameter identification
A novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China and it is suggested that the transmission of individuals should be greatly controlled with high isolation rate by the government.
Modeling and forecasting the early evolution of the Covid-19 pandemic in Brazil
Short and long term forecasts show that the social distancing policy imposed by the government is able to flatten the pattern of infection of the COVID-19 pandemic, but if this policy does not last enough time, it is only able to shift the peak of infection into the future keeping the value of the peak in almost the same value.