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

Reproduction Number ◽

Approximate Solutions ◽

Sir Model ◽

Logistic Growth ◽

Exact Results ◽

Logistic Curve ◽

AbstractApproximate solutions of SIR equations are given, based on a logistic growth curve in the Biology. These solutions are applied to fix the basic reproduction number α 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.

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

J ◽

10.3390/j4020008 ◽

2021 ◽

Vol 4 (2) ◽

pp. 86-100

Author(s):

Nita H. Shah ◽

Ankush H. Suthar ◽

Ekta N. Jayswal ◽

Ankit Sikarwar

Keyword(s):

Reproduction Number ◽

Transmission Rate ◽

Sir Model ◽

Time Dependent ◽

Contact Rate ◽

Distribution Maps ◽

Fundamental Parameters ◽

Different Order ◽

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.

Threshold Dynamics of a Huanglongbing Model with Logistic Growth in Periodic Environments

Abstract and Applied Analysis ◽

10.1155/2014/841367 ◽

2014 ◽

Vol 2014 ◽

pp. 1-10 ◽

Cited By ~ 3

Author(s):

Jianping Wang ◽

Shujing Gao ◽

Yueli Luo ◽

Dehui Xie

Keyword(s):

Reproduction Number ◽

Logistic Growth ◽

Threshold Dynamics ◽

Global Dynamics ◽

Globally Asymptotically Stable ◽

Linear Integral ◽

The Impact ◽

Disease Free ◽

We analyze the impact of seasonal activity of psyllid on the dynamics of Huanglongbing (HLB) infection. A new model about HLB transmission with Logistic growth in psyllid insect vectors and periodic coefficients has been investigated. It is shown that the global dynamics are determined by the basic reproduction numberR0which is defined through the spectral radius of a linear integral operator. IfR0< 1, then the disease-free periodic solution is globally asymptotically stable and ifR0> 1, then the disease persists. Numerical values of parameters of the model are evaluated taken from the literatures. Furthermore, numerical simulations support our analytical conclusions and the sensitive analysis on the basic reproduction number to the changes of average and amplitude values of the recruitment function of citrus are shown. Finally, some useful comments on controlling the transmission of HLB are given.

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

International Journal of Modern Physics C ◽

10.1142/s0129183121500406 ◽

2020 ◽

pp. 2150040

Author(s):

I. F. F. Dos Santos ◽

G. M. A. Almeida ◽

F. A. B. F. De Moura

Keyword(s):

Reproduction Number ◽

Sir Model ◽

The State ◽

Epidemic Dynamics ◽

Historical Series ◽

Input Parameters ◽

Number Formula ◽

Near Future ◽

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.

Analysis and Prediction of COVID-19 Characteristics Using a Birth-and-Death Model

10.1101/2020.06.23.20138719 ◽

2020 ◽

Author(s):

Narayanan C. Viswanath

Keyword(s):

Mathematical Modeling ◽

Infectious Diseases ◽

Explicit Expression ◽

Stationary Point ◽

Reproduction Number ◽

Sir Model ◽

Expected Number ◽

Infection Period ◽

AbstractIts spreading speed together with the risk of fatality might be the main characteristic that separates COVID-19 from other infectious diseases in our recent history. In this scenario, mathematical modeling for predicting the spread of the disease could have great value in containing the disease. Several very recent papers have contributed to this purpose. In this study we propose a birth-and-death model for predicting the number of COVID-19 active cases. It relation to the Susceptible-Infected-Recovered (SIR) model has been discussed. An explicit expression for the expected number of active cases helps us to identify a stationary point on the infection curve, where the infection ceases increasing. Parameters of the model are estimated by fitting the expressions for active and total reported cases simultaneously. We analyzed the movement of the stationary point and the basic reproduction number during the infection period up to the 20th of April 2020. These provide information about the disease progression path and therefore could be really useful in designing containment strategies.

Local Dynamics of an SVIR Epidemic Model with Logistic Growth

CAUCHY ◽

10.18860/ca.v6i3.9891 ◽

2020 ◽

Vol 6 (3) ◽

pp. 122-132

Author(s):

Joko Harianto ◽

Inda Puspita Sari

Keyword(s):

Stability Analysis ◽

Equilibrium Point ◽

Local Stability ◽

Reproduction Number ◽

Endemic Equilibrium ◽

Logistic Growth ◽

Asymptotically Stable ◽

Local Stability Analysis ◽

Discussion of local stability analysis of SVIR models in this article is included in the scope of applied mathematics. The purpose of this discussion was to provide results of local stability analysis that had not been discussed in some articles related to the SVIR model. The SVIR models discussed in this article involve logistics growth in the vaccinated compartment. The results obtained, i.e. if the basic reproduction number less than one and m is positive, then there is one equilibrium point i.e. E0 is locally asymptotically stable. In the field of epidemiology, this means that the disease will disappear from the population. However, if the basic reproduction number more than one and b1 more than b, then there are two equilibrium points i.e. disease-free equilibrium point denoted by E0 and the endemic equilibrium point denoted by E1*. In this case the endemic equilibrium point E1* is locally asymptotically stable. In the field of epidemiology, this means that the disease will remain in the population. The numerical simulation supports these results.

An Age and Space Structured SIR Model Describing the Covid-19 Pandemic

10.1101/2020.05.15.20103317 ◽

2020 ◽

Cited By ~ 1

Author(s):

Rinaldo M Colombo ◽

Mauro Garavello ◽

Francesca Marcellini ◽

Elena Rossi

Keyword(s):

Epidemic Model ◽

Reproduction Number ◽

Sir Model ◽

Qualitative Properties ◽

Numerical Integrations ◽

Key Features ◽

Virus Spreading ◽

We present an epidemic model capable of describing key features of the present Covid-19 pandemic. While capturing several qualitative properties of the virus spreading, it allows to compute the basic reproduction number, the number of deaths due to the virus and various other statistics. Numerical integrations are used to illustrate the relevance of quarantine and the role of care houses.

An early estimation of the number of affected people in South Asia due to Covid-19 pandemic using susceptible, infected and recover model

International Journal of Modern Physics C ◽

10.1142/s0129183120501405 ◽

2020 ◽

Vol 31 (10) ◽

pp. 2050140

Author(s):

Md. Enamul Hoque

Keyword(s):

Simple Model ◽

South Asia ◽

South Asian ◽

Numerical Solutions ◽

Reproduction Number ◽

Sir Model ◽

Asian Countries ◽

Susceptible Population ◽

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 Bangladesh, India, Pakistan and compared with that of China. Numerical solutions are used to obtain the value of parameters for the SIR model. It is predicted that the active case in Pakistan due to the SARS-CoV-2 will be comparable with that in China whereas it will be low for Bangladesh and India. The basic reproduction number, with fluctuations, for South Asian countries are predicted to be less than that of China. The susceptible population is also estimated to be under a million for Bangladesh and India but it becomes very large for Pakistan.

Assessing inference of the basic reproduction number in an SIR model incorporating a growth-scaling parameter

Statistics in Medicine ◽

10.1002/sim.7935 ◽

2018 ◽

Vol 37 (29) ◽

pp. 4490-4506 ◽

Cited By ~ 2

Author(s):

Tapiwa Ganyani ◽

Christel Faes ◽

Gerardo Chowell ◽

Niel Hens

Keyword(s):

Reproduction Number ◽

Sir Model ◽

Scaling Parameter ◽

Growth Scaling ◽

ANALYSIS OF AN AGE-STRUCTURED HIV-1 INFECTION MODEL WITH LOGISTIC TARGET CELL GROWTH

Journal of Biological System ◽

10.1142/s0218339020500229 ◽

2020 ◽

Vol 28 (04) ◽

pp. 927-944

Author(s):

HUIJUAN LIU ◽

FEI XU ◽

JIA-FANG ZHANG

Keyword(s):

Reproduction Number ◽

Logistic Growth ◽

Infection Model ◽

Target Cells ◽

Asymptotically Stable ◽

Globally Asymptotically Stable ◽

Age Structured ◽

Hiv 1 ◽

In this work, we construct an age-structured HIV-1 infection model to investigate the interplay between [Formula: see text] cells and viruses. In our model, we assume that the variations in the death rate of productively infected [Formula: see text] cells and the production rate of virus in infected cells are all age-dependent, and the target cells follow logistic growth. We perform mathematical analysis and prove the persistence of the semi-flow of the system. We calculate the basic reproduction number and prove the local and global stability of the steady states. We show that if the basic reproduction number is less than one, the disease-free equilibrium is globally asymptotically stable, and if the basic reproduction number is greater than one, the infected steady state is locally asymptotically stable.

The pluses and minuses of 0

Journal of The Royal Society Interface ◽

10.1098/rsif.2007.1031 ◽

2007 ◽

Vol 4 (16) ◽

pp. 949-961 ◽

Cited By ~ 63

Author(s):

M.G Roberts

Keyword(s):

Reproduction Number ◽

Central Place ◽

Sir Model ◽

Direct Measure ◽

Control Effort ◽

Epidemic Theory ◽

The concept of the basic reproduction number ( 0 ) occupies a central place in epidemic theory. The value of 0 determines the proportion of the population that becomes infected over the course of a (modelled) epidemic. In many models, (i) an endemic infection can persist only if 0 >1, (ii) the value of 0 provides a direct measure of the control effort required to eliminate the infection, and (iii) pathogens evolve to maximize their value of 0 . These three statements are not universally true. In this paper, some exceptions to them are discussed, based on the extensions of the SIR model.