A Logistic Curve in the SIR Model and Its Application to Deaths by COVID-19 in Japan

@article{Shigemoto2020ALC,
  title={A Logistic Curve in the SIR Model and Its Application to Deaths by COVID-19 in Japan},
  author={Kazuyasu Shigemoto and T. Saito},
  journal={medRxiv},
  year={2020}
}
Approximate solutions of SIR equations are given, ased on a logistic growth curve in the Biology. These solutions are applied to fix the basic reproduction number $alpha$ and the removed ratio $c$, especially from data of accumulated number of deaths in Japan COVID-19. We then discuss the end of the epidemic. These logistic curve results are compared with the exact results of the SIR model. } 
An Application of Logistic Formula to Deaths by COVID-19 in Japan
TLDR
A logistic formula in biology is applied to analyze deaths by COVID-19 for both of the first and the second waves in Japan, and the meaning of population N in an epidemic is discussed.
A Logistic Formula in Biology and Its Application to Deaths by the Third Wave of COVID-19 in Japan
  • T. Saito
  • Business, Mathematics
    medRxiv
  • 2021
TLDR
A logistic formula in biology is applied to analyze the third wave of COVID-19 in Japan and shows good results in terms of predictability and efficiency.
Logistic Formula in Biology and Its Application to COVID-19 in Japan
A logistic formula in biology is applied, as the first principle, to analyze the second and third waves of COVID=19 in Japan.
Variants of SARS-COV-2 and the Death Toll
TLDR
Why the number of deaths in SARS-COV-2 is so small, compared with high cases, around the infection peak, when the basic reproduction number is very large is considered.
SEIRDQ: A COVID-19 case projection modeling framework using ANN to model quarantine
TLDR
A novel approach to model the evolution of CO VID-19 pandemic and predict the daily COVID-19 cases by adding additional compartments to capture recovered, dead and quarantined cases using an Artificial Neural Network.
Fractional-Order Logistic Differential Equation with Mittag–Leffler-Type Kernel
In this paper, we consider the Prabhakar fractional logistic differential equation. By using appropriate limit relations, we recover some other logistic differential equations, giving representations
Power series solution of the fractional logistic equation
  • I. Area, J. Nieto
  • Mathematics
    Physica A: Statistical Mechanics and its Applications
  • 2021
Fractional Euler numbers and generalized proportional fractional logistic differential equation
  • J. Nieto
  • Mathematics
    Fractional calculus & applied analysis
  • 2022
We solve a logistic differential equation for generalized proportional Caputo fractional derivative. The solution is found as a fractional power series. The coefficients of that power series are

References

SHOWING 1-10 OF 11 REFERENCES
The Mathematics of Infectious Diseases
TLDR
Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Mathematical models of SIR disease spread with combined non-sexual and sexual transmission routes
TLDR
A number of low-dimensional models which are appropriate for a range of assumptions for how a disease will spread if it has sexual transmission through a sexual contact network combined with some other transmission mechanism, such as direct contact or vectors are developed.
Mathematical Modeling of Epidemic Diseases; A Case Study of the COVID-19 Coronavirus
TLDR
It is shown how social measures such as distancing, regional lockdowns, quarantine and global public health vigilance, influence the model parameters, which can eventually change the mortality rates and active contaminated cases over time, in the real world.
Rich dynamics of an SIR epidemic model
This paper aims to study an SIR epidemic model with an asymptotically homogeneous transmission function. The stability of the disease-free and the endemic equilibrium is addressed. Numerical
Mathematical modelling of infectious diseases.
TLDR
These principles of mathematical models, which allow us to extrapolate from current information about the state and progress of an outbreak, to predict the future and to quantify the uncertainty in these predictions, are illustrated in relation to the current H1N1 epidemic.
Epidemic Models and the Dynamics of Infectious Diseases
TLDR
The study of epidemics has a long history with a vast variety of models and explanations for the spread and cause of epidemic outbreaks, and Hippocrates wrote that one’s temperament, personal habits and environment were important factors — not unreasonable even today.
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.
‘A’
  • P. Alam
  • Medicine
    Composites Engineering: An A–Z Guide
  • 2021
TLDR
A fluorescence-imaging-based endoscopic capsule that automates the detection process of colorectal cancer was designed and developed in the lab and offered great possibilities for future applicability in selective and specific detection of other fluorescently labelled cancers.
...
...