scholarly journals Dynamics of an SIR-Based COVID-19 Model With Linear Incidence Rate, Nonlinear Removal Rate, and Public Awareness

2021 ◽  
Vol 9 ◽  
Author(s):  
Abdelhamid Ajbar ◽  
Rubayyi T. Alqahtani ◽  
Mourad Boumaza
Keyword(s):  
Incidence Rate ◽  
Reproduction Number ◽  
Removal Rate ◽  
Public Awareness ◽  
Sir Model ◽  
Hopf Bifurcations ◽  
Nonlinear Phenomena ◽  
Hospital Bed ◽  
Population Ratio ◽  
Effects Of Media

The paper studies the dynamics of the classical susceptible-infectious-removed (SIR) model when applied to the transmission of COVID-19 disease. The model includes the classical linear incidence rate but considers a nonlinear removal rate that depends on the hospital-bed population ratio. The model also includes the effects of media on public awareness. We prove that when the basic reproduction number is less than unity the model can exhibit a number of nonlinear phenomena including saddle-node, backward, and Hopf bifurcations. The model is fitted to COVID-19 data pertinent to Saudi Arabia. Numerical simulations are provided to supplement the theoretical analysis and delineate the effects of hospital-bed population ratio and public awareness on the control of the disease.

scholarly journals The SIR model towards the data

2021 ◽  
Vol 136 (8) ◽  
Author(s):  
Ignazio Lazzizzera
Keyword(s):  
Generation Time ◽  
Reproduction Number ◽  
Removal Rate ◽  
Sir Model ◽  
Infectious Period ◽  
Third Wave ◽  
Real Numbers ◽  
The Third ◽  
Study Case ◽  
Good Agreement

AbstractIn this work, the SIR epidemiological model is reformulated so to highlight the important effective reproduction number, as well as to account for the generation time, the inverse of the incidence rate, and the infectious period (or removal period), the inverse of the removal rate. The aim is to check whether the relationships the model poses among the various observables are actually found in the data. The study case of the second through the third wave of the Covid-19 pandemic in Italy is taken. Given its scale invariance, initially the model is tested with reference to the curve of swab-confirmed infectious individuals only. It is found to match the data, if the curve of the removed (that is healed or deceased) individuals is assumed underestimated by a factor of about 3 together with other related curves. Contextually, the generation time and the removal period, as well as the effective reproduction number, are obtained fitting the SIR equations to the data; the outcomes prove to be in good agreement with those of other works. Then, using knowledge of the proportion of Covid-19 transmissions likely occurring from individuals who didn’t develop symptoms, thus mainly undetected, an estimate of the real numbers of the epidemic is obtained, looking also in good agreement with results from other, completely different works. The line of this work is new, and the procedures, computationally really inexpensive, can be applied to any other national or regional case besides Italy’s study case here.

scholarly journals Tracking and Predicting COVID-19 Epidemic in China Mainland

2020 ◽  
Author(s):  
Haoxuan Sun ◽  
Yumou Qiu ◽  
Han Yan ◽  
Yaxuan Huang ◽  
Yuru Zhu ◽  
...  
Keyword(s):  
Reproduction Number ◽  
Removal Rate ◽  
Public Awareness ◽  
Hubei Province ◽  
Control Measures ◽  
Slowing Down ◽  
Substantial Decline ◽  
China Mainland ◽  
High Level ◽  
Removal Model

AbstractBy proposing a varying coefficient Susceptible-Infected-Removal model (vSIR), we track the epidemic of COVID-19 in 30 provinces in China and 15 cities in Hubei province, the epicenter of the outbreak. It is found that the spread of COVID-19 has been significantly slowing down within the two weeks from January 27 to February 10th with 87.0% and 84.3% reductions in the reproduction number R0 among the 30 provinces and 15 Hubei cities, respectively. This suggests the extreme control measures implemented since January 23, which include cutting off Wuhan and many other cities and towns, a great public awareness and high level of self isolation at home, have contributed to a substantial decline in the reproductivity of the COVID-19 in China. We predict that Hubei province will reach its peak between February 20 and 22, 2020, and if the removal rate can be increased to 0.1, the epidemic outside Hubei province will end in May 2020, and inside Hubei in early June.

scholarly journals Fractional SIR-Model for Estimating Transmission Dynamics of COVID-19 in India

J ◽  
2021 ◽  
Vol 4 (2) ◽  
pp. 86-100
Author(s):  
Nita H. Shah ◽  
Ankush H. Suthar ◽  
Ekta N. Jayswal ◽  
Ankit Sikarwar
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Time Dependent ◽  
Contact Rate ◽  
Distribution Maps ◽  
Fundamental Parameters ◽  
Different Order ◽  
The Basic Reproduction Number

In this article, a time-dependent susceptible-infected-recovered (SIR) model is constructed to investigate the transmission rate of COVID-19 in various regions of India. The model included the fundamental parameters on which the transmission rate of the infection is dependent, like the population density, contact rate, recovery rate, and intensity of the infection in the respective region. Looking at the great diversity in different geographic locations in India, we determined to calculate the basic reproduction number for all Indian districts based on the COVID-19 data till 7 July 2020. By preparing district-wise spatial distribution maps with the help of ArcGIS 10.2, the model was employed to show the effect of complete lockdown on the transmission rate of the COVID-19 infection in Indian districts. Moreover, with the model's transformation to the fractional ordered dynamical system, we found that the nature of the proposed SIR model is different for the different order of the systems. The sensitivity analysis of the basic reproduction number is done graphically which forecasts the change in the transmission rate of COVID-19 infection with change in different parameters. In the numerical simulation section, oscillations and variations in the model compartments are shown for two different situations, with and without lockdown.

The threshold for a stochastic within-host CHIKV virus model with saturated incidence rate

2021 ◽  
pp. 2150042
Author(s):  
C. Gokila ◽  
M. Sambath
Keyword(s):  
Lyapunov Function ◽  
Incidence Rate ◽  
Stationary Distribution ◽  
Reproduction Number ◽  
Threshold Value ◽  
Saturated Incidence Rate ◽  
Number Formula ◽  
Saturated Incidence ◽  
Virus Model ◽  
Global Positive Solution

This paper deals with stochastic Chikungunya (CHIKV) virus model along with saturated incidence rate. We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct. We also discuss about the existence of a unique ergodic stationary distribution of the model, through a suitable Lyapunov function. The stationary distribution validates the occurrence of disease; through that, we find the threshold value for prevail and disappear of disease within host. With the help of numerical simulations, we validate the stochastic reproduction number [Formula: see text] as stated in our theoretical findings.

Estimation of the number of affected people due to the Covid-19 pandemic using susceptible, infected and recover model

2020 ◽  
Vol 31 (08) ◽  
pp. 2050111
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model

The Susceptible, Infected and Recover (SIR) model is a very simple model to estimate the dynamics of an epidemic. In the current pandemic due to Covid-19, the SIR model has been used to estimate the dynamics of infection for various infected countries. Numerical solutions are used to obtain the value of parameters for the SIR model. The maximum and minimum basic reproduction number (14.5 and 2.3) are predicted to be in Turkey and China, respectively.

Global Dynamics of a Parasite-Host Model with Nonlinear Incidence Rate

2015 ◽  
Vol 25 (08) ◽  
pp. 1550102 ◽  
Author(s):  
Yilei Tang
Keyword(s):  
Incidence Rate ◽  
Global Attractor ◽  
Exponential Function ◽  
Limit Cycles ◽  
Hopf Bifurcations ◽  
Global Dynamics ◽  
Nonlinear Incidence Rate ◽  
Nonlinear Incidence ◽  
Dynamical Behaviors ◽  
Fractional Function

The paper is concerned with the effect of a nonlinear incidence rate Sp Iq on dynamical behaviors of a parasite-host model. It is shown that the global attractor of the parasite-host model is an equilibrium if q = 1, which is similar to that of the parasite-host model with a nonlinear incidence rate of the fractional function [Formula: see text]. However, when q is greater than one, more positive equilibria appear and limit cycles arise from Hopf bifurcations at the positive equilibria for the model with the incidence rate Sp Iq. It reveals that the nonlinear incidence rate of the exponential function Sp Iq for generic p and q can lead to more complicated and richer dynamics than the bilinear incidence rate or the fractional incidence rate for this model.

Evolution of SARS-CoV-2 in the state of Alagoas-Brazil via an adaptive SIR model

2020 ◽  
pp. 2150040
Author(s):  
I. F. F. Dos Santos ◽  
G. M. A. Almeida ◽  
F. A. B. F. De Moura
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Sir Model ◽  
The State ◽  
Epidemic Dynamics ◽  
Historical Series ◽  
Input Parameters ◽  
Number Formula ◽  
Near Future ◽  
The Basic Reproduction Number

We investigate the spreading of SARS-CoV-2 in the state of Alagoas, northeast of Brazil, via an adaptive susceptible-infected-removed (SIR) model featuring dynamic recuperation and propagation rates. Input parameters are defined based on data made available by Alagoas Secretary of Health from April 19, 2020 on. We provide with the evolution of the basic reproduction number [Formula: see text] and reproduce the historical series of the number of confirmed cases with less than [Formula: see text] error. We offer predictions, from November 16 forward, over the epidemic situation in the near future and show that it will keep decelerating. Furthermore, the same model can be used to study the epidemic dynamics in other countries with great easiness and accuracy.

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