# 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…

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## 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

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

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

- MathematicsScientific reports
- 2020

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.

### Exact analytical solutions of the Susceptible-Infected-Recovered (SIR) epidemic model and of the SIR model with equal death and birth rates

- MathematicsAppl. Math. Comput.
- 2014

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

- MedicinemedRxiv
- 2020

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

- Mathematics
- 2011

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

- Mathematics
- 1992

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,…

### Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?

- MathematicsChaos, Solitons & Fractals
- 2020

### Numerical modeling and theoretical analysis of a nonlinear advection-reaction epidemic system

- MathematicsComput. Methods Programs Biomed.
- 2020

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

- EconomicsChaos, Solitons & Fractals
- 2020

### A contribution to the mathematical theory of epidemics

- Medicine, Mathematics
- 1927

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.