scholarly journals Forecasting the Long-Term Trends of Coronavirus Disease 2019 (COVID-19) Epidemic Using the Susceptible-Infectious-Recovered (SIR) Model

2021 ◽  
Vol 13 (3) ◽  
pp. 668-684
Author(s):  
Agus Kartono ◽  
Savira Vita Karimah ◽  
Setyanto Tri Wahyudi ◽  
Ardian Arif Setiawan ◽  
Irmansyah Sofian
Keyword(s):  
Simple Model ◽  
Time Evolution ◽  
Reduction Process ◽  
Sir Model ◽  
Parameters Estimation ◽  
Actual Data ◽  
Logistic Growth ◽  
Susceptible Population ◽  
Basic Characteristics ◽  
Sequential Reduction

A simple model for predicting Coronavirus Disease 2019 (COVID-19) epidemic is presented in this study. The prediction model is presented based on the classic Susceptible-Infectious-Recovered (SIR) model, which has been widely used to describe the epidemic time evolution of infectious diseases. The original version of the Kermack and McKendrick model is used in this study. This included the daily rates of infection spread by infected individuals when these individuals interact with a susceptible population, which is denoted by the parameter β, while the recovery rates to determine the number of recovered individuals is expressed by the parameter γ. The parameters estimation of the three-compartment SIR model is determined through using a mathematical sequential reduction process from the logistic growth model equation. As the parameters are the basic characteristics of epidemic time evolution, the model is always tested and applied to the latest actual data of confirmed COVID-19 cases. It seems that this simple model is still reliable enough to describe the dynamics of the COVID-19 epidemic, not only qualitatively but also quantitatively with a high degree of correlation between actual data and prediction results. Therefore, it is possible to apply this model to predict cases of COVID-19 in several countries. In addition, the parameter characteristics of the classic SIR model can provide information on how these parameters reflect the efforts by each country to prevent the spread of the COVID-19 outbreak. This is clearly seen from the changes of the parameters shown by the classic SIR model.

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

2020 ◽  
Vol 31 (10) ◽  
pp. 2050140
Author(s):  
Md. Enamul Hoque
Keyword(s):  
Simple Model ◽  
South Asia ◽  
South Asian ◽  
Basic Reproduction Number ◽  
Numerical Solutions ◽  
Reproduction Number ◽  
Sir Model ◽  
Asian Countries ◽  
Susceptible Population ◽  
The Basic Reproduction Number

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.

scholarly journals Qualitative analysis and optimal control of an SIR model with logistic growth, non-monotonic incidence and saturated treatment

2021 ◽  
Author(s):  
Jayanta Kumar Ghosh ◽  
Prahlad Majumdar ◽  
Uttam Ghosh
Keyword(s):  
Optimal Control ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Sir Model ◽  
Logistic Growth ◽  
Treatment Rate ◽  
Globally Asymptotically Stable ◽  
Susceptible Population ◽  
Saturated Treatment

This paper describes an SIR model with logistic growth rate of susceptible population, non-monotonic incidence rate and saturated treatment rate. The existence and stability analysis of equilibria have been investigated. It has been shown that the disease free equilibrium point ( DFE ) is globally asymptotically stable if the basic reproduction number is less than unity and the transmission rate of infection less than some threshold. The system exhibits the transcritical bifurcation at DFE with respect to the cure rate. We have also found the condition for occurring the backward bifurcation, which implies the value of basic reproduction number less than unity is not enough to eradicate the disease. Stability or instability of different endemic equilibria has been shown analytically. The system also experiences the saddle-node and Hopf bifurcation. The existence of Bogdanov - Takens bifurcation ( BT ) of co-dimension 2 has been investigated which has also been shown through numerical simulations. Here we have used two control functions, one is vaccination control and other is treatment control. We have solved the optimal control problem both analytically and numerically. Finally, the efficiency analysis has been used to determine the best control strategy among vaccination and treatment.

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.

The effect of barotropic instability on the nonlinear evolution of a Rossby-wave critical layer

1989 ◽  
Vol 207 ◽  
pp. 231-266 ◽  
Author(s):  
Peter H. Haynes
Keyword(s):  
Simple Model ◽  
Numerical Model ◽  
Time Evolution ◽  
Rossby Wave ◽  
Nonlinear Evolution ◽  
Basic Flow ◽  
Critical Layer ◽  
Barotropic Instability ◽  
Long Wavelength ◽  
Subsequent Time

A study of the flow within the critical layer of a forced Rossby-wave is made, using a high-resolution numerical model. The possibility of growth of disturbances through barotropic instability and the extent to which these disturbances modify the subsequent time evolution is of particular interest. The flow is characterized by a parameter μ, equal to the cross-stream lengthscale divided by a downstream wavelength. In the long-wavelength case, μ [Lt ] 1, where there is a clear conceptual division between the instability and the basic flow, the results of the simulation confirm the importance of the growing and saturating disturbances in rearranging the vorticity within the critical layer. When the wavelength is not so long, the distinction between the instability and the straightforward time evolution of the basic flow is less clear. Nonetheless for μ < 0.25 the ultimate evolution is still sensitive to the details of the initial perturbations and in this sense the flow may be regarded as being unstable. The time-integrated absorptivity of the critical layer may be considerably increased by the effects of the instability, sometimes to three or four times that predicted by the Stewartson-Warn-Warn solution. The nature of the flow, at least during the period in which the dynamics are essentially inviscid, does not seem to change when higher harmonics to the forced wave are resonant. The behaviour seen in Béland's (1976) numerical model is re-examined in the light of these findings. A simple model of the redistribution of vorticity by the unstable disturbances is formulated, and its predictions are shown to agree well with the numerical simulations.

Localisation of Carriers in Porous Silicon

1996 ◽  
Vol 452 ◽  
Author(s):  
I. Mihalcescu ◽  
J. C. Vial ◽  
R. Romestain
Keyword(s):  
Simple Model ◽  
Porous Silicon ◽  
Temperature Variation ◽  
Time Evolution ◽  
Decay Time ◽  
Additional Assumption ◽  
Shape Evolution ◽  
Photoluminescence Intensity ◽  
Photoluminescence Decay ◽  
Strong Localization

AbstractWe analyze the intensity and decay time evolution of the porous silicon luminescence upon anodic oxidation, aging, chemiral thinning and temperature variation. Strong analogies are pointed out for the photoluminescence intensity as well as for the photoluminescence decay shape evolution. They are interpreted by the variation of the extension of the carrier wavefunction induced by the modification of potential barrier efficiencies. No additional assumption such as hopping of carriers was necessary to explain the decay shapes well fitted by stretched exponential. On the contrary our observations and our simple model are in favor of a strong localization of carriers. Some experimental results are revisited within the frame of this model.

Approximations to the time evolution of an Izhikevich neuron

2014 ◽  
Vol 25 (10) ◽  
pp. 1450052 ◽  
Author(s):  
August Romeo ◽  
Hans Supèr
Keyword(s):  
Simple Model ◽  
Power Series ◽  
Small Parameter ◽  
Time Evolution ◽  
Scale Effects ◽  
Spiking Neuron ◽  
Elementary Functions ◽  
Constant Input ◽  
Parameter Expansion

Possible ways of obtaining information about the solutions of Izhikevich's "simple model" for a spiking neuron are considered. The method of power series in time is reviewed. From a different viewpoint, in the case of constant input and weak recovery scale effects, advantage is taken of a small-parameter expansion. The obtained approximations can be expressed in terms of elementary functions.

scholarly journals CoSIR: Managing an Epidemic via Optimal Adaptive Control of Transmission Policy

2020 ◽  
Author(s):  
Harsh Maheshwari ◽  
Shreyas Shetty ◽  
Nayana Bannur ◽  
Srujana Merugu
Keyword(s):  
Adaptive Control ◽  
Control Method ◽  
Transmission Rate ◽  
Analytical Framework ◽  
Sir Model ◽  
Practical Implementation ◽  
Stable Equilibrium Point ◽  
Transmission Control ◽  
Susceptible Population ◽  
Predator Prey Model

AbstractShaping an epidemic with an adaptive contact restriction policy that balances the disease and socioeconomic impact has been the holy grail during the COVID-19 pandemic. Most of the existing work on epidemiological models [40, 11, 17, 7] focuses on scenario-based forecasting via simulation but techniques for explicit control of epidemics via an analytical framework are largely missing. In this paper, we consider the problem of determining the optimal policy for transmission control assuming SIR dynamics [28], which is the most widely used epidemiological paradigm. We first demonstrate that the SIR model with infectious patients and susceptible contacts (i.e., product of transmission rate and susceptible population) interpreted as predators and prey respectively reduces to a Lotka-Volterra (LV) predator-prey model [8]. The modified SIR system (LVSIR) has a stable equilibrium point, an “energy” conservation property, and exhibits bounded cyclic behaviour similar to an LV system. This mapping permits a theoretical analysis of the control problem supporting some of the recent simulation-based studies [16, 29] that point to the benefits of periodic interventions. We use a control-Lyapunov approach to design adaptive control policies (CoSIR) to nudge the SIR model to the desired equilibrium that permits ready extensions to richer compartmental models. We also describe a practical implementation of this transmission control method by approximating the ideal control with a finite, but a time-varying set of restriction levels and provide simulation results to demonstrate its efficacy.

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