Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case

@article{Schlickeiser2021AnalyticalSO,
  title={Analytical solution of the SIR-model for the temporal evolution of epidemics: part B. Semi-time case},
  author={Reinhard Schlickeiser and Martin Kr{\"o}ger},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2021},
  volume={54}
}
The earlier analytical analysis (part A) of the susceptible–infectious–recovered (SIR) epidemics model for a constant ratio k of infection to recovery rates is extended here to the semi-time case which is particularly appropriate for modeling the temporal evolution of later (than the first) pandemic waves when a greater population fraction from the first wave has been infected. In the semi-time case the SIR model does not describe the quantities in the past; instead they only hold for times… 

SIR-Solution for Slowly Time-Dependent Ratio between Recovery and Infection Rates

The temporal evolution of pandemics described by the susceptible-infectious-recovered (SIR)-compartment model is sensitively determined by the time dependence of the infection (a(t)) and recovery

Analytical Modeling of the Temporal Evolution of Epidemics Outbreaks Accounting for Vaccinations

With the vaccination against Covid-19 now available, how vaccination campaigns influence the mathematical modeling of epidemics is quantitatively explored. In this paper, the standard

Forecast for the second Covid-19 wave based on the improved SIR model with a constant ratio of recovery to infection rate

We start out by deriving simple analytic expressions for all measurable amounts of cases and fatalities during a pandemic evolution exhibiting multiple waves, described by the semi-time SIR model.

Verification of the accuracy of the SIR model in forecasting based on the improved SIR model with a constant ratio of recovery to infection rate by comparing with monitored second wave data

TLDR
Most recent data serves to demonstrate the successful forecast and high accuracy of the SIR model in predicting the evolution of pandemic outbreaks as long as the assumption underlying the analysis, an unchanged situation of the distribution of variants of concern and the fatality fraction, do not change dramatically during a wave.

Forecast of omicron wave time evolution

TLDR
It seems that the German health system can barely cope with the omicron wave avoiding triage decisions, which is about one order of magnitude smaller than the beta fatality rate and total number.

An extended epidemic model with vaccination: Weak-immune SIRVI

  • M. Turkyilmazoglu
  • Mathematics
    Physica A: Statistical Mechanics and its Applications
  • 2022

Multi-Hamiltonian structure of the epidemics model accounting for vaccinations and a suitable test for the accuracy of its numerical solvers

We derive a generalized Hamiltonian formalism for a modified susceptible–infectious–recovered/removed (SIR) epidemic model taking into account the population V of vaccinated persons. The resulting

Asymptotic analysis of the SIR model. Applications to COVID-19 modelling

TLDR
The parametric solution of the SIR model in terms of quadratures is derived and a simple analytical asymptotic solution for the I-variable is demonstrated, which can be used successfully for parametric estimation either in stand-alone mode or as a preliminary step in theParametric estimation using numerical inversion of theparametric solution.

Discrete-time Layered-network Epidemics Model with Time-varying Transition Rates and Multiple Resources

This paper studies a discrete-time time-varying multi-layer networked SIWS (susceptible-infected-water-susceptible) model with multiple resources under both single-virus and competing multi-virus

References

SHOWING 1-10 OF 49 REFERENCES

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 approximately universal shapes of epidemic curves in the Susceptible-Exposed-Infectious-Recovered (SEIR) model

TLDR
The approach of Harko et al. is generalised to obtain an approximate semi-analytical solution of the Susceptible-Exposed-Infectious-Recovered (SEIR) model, implying an approximate characteristic timescale that is universal to all SEIR models, which only depends on the basic reproduction number and initial fraction of the population that is infectious.

Dynamics of COVID-19 pandemic at constant and time-dependent contact rates

TLDR
A model of the spread of COVID-19 considers a scenario based on typical social behaviours, in which r_C first decreases in response to a surge of daily new cases, forcing people to self-isolate, and then slowly increases when people gradually accept higher risk.

Susceptible-infected-recovered and susceptible-exposed-infected models

Two stochastic epidemic lattice models, the susceptible-infected-recovered and the susceptible-exposed-infected models, are studied on a Cayley tree of coordination number k. The spreading of the

Automata network SIR models for the spread of infectious diseases in populations of moving individuals

Automata network SIR models for the spread of infectious diseases are studied. The local rule consists of two subrules. The first one, applied sequentially, describes the motion of the individuals,

Estimating the infection horizon of COVID-19 in eight countries with a data-driven approach

A contribution to the mathematical theory of epidemics

TLDR
The present communication discussion will be limited to the case in which all members of the community are initially equally susceptible to the disease, and it will be further assumed that complete immunity is conferred by a single infection.