SIR model for propagation of COVID-19 in the Paraíba's State (Brazil)

2021 ◽  
Vol 2 (2) ◽  
pp. 39-48
Author(s):  
Célia Maria Rufino Franco ◽  
Renato Ferreira Dutra
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Health Department ◽  
Sir Model ◽  
Euler Method ◽  
Control Measures ◽  
System Of Differential Equations ◽  
Infection Transmission ◽  
Epidemic Dynamics ◽  
The Town

This work aims to apply the SIR-type compartmental model (Susceptible - Infected - Removed) in the evolution of Covid-19 in Paraíba's State and Campina Grande City. For that, the parameters of the model were considered to be variable during time evolution, within an appropriate range. The system of differential equations was solved numerically using the Euler method. The parameters were obtained by adjusting the model to the infected data provided by the Paraíba Health Department. According to the results obtained, the model describes the infected population well. There was a reduction in the effective reproduction number in Paraíba and the town of Campina Grande. It is noteworthy that understanding the dynamics of infection transmission and evaluating the effectiveness of control measures is crucial to assess the potential for sustained transmission to occur in new areas. The model can also be applied to describe epidemic dynamics in other regions and countries. 

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.

scholarly journals Is Nigeria really on top of COVID-19? Message from effective reproduction number

2020 ◽  
Author(s):  
Adeshina Israel Adekunle ◽  
Oyelola Adegboye ◽  
Ezra Gayawan ◽  
Emma McBryde
Keyword(s):  
Public Health ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Credible Interval ◽  
Control Measures ◽  
Maximum Value ◽  
Intervention Measures ◽  
Death Cases ◽  
Epidemiological Parameters

Following the importation of Covid-19 into Nigeria on the 27 February 2020 and then the outbreak, the question is: how do we anticipate the progression of the ongoing epidemics following all the intervention measures put in place? This kind of question is appropriate for public health responses and it will depend on the early estimates of the key epidemiological parameters of the virus in a defined population. In this study, we combined a likelihood-based method using a Bayesian framework and compartmental model of the epidemic of Covid-19 in Nigeria to estimate the effective reproduction number (R(t)) and basic reproduction number (R_0). This also enables us to estimate the daily transmission rate (β) that determines the effect of social distancing. We further estimate the reported fraction of symptomatic cases. The models are applied to the NCDC data on Covid-19 symptomatic and death cases from 27 February 2020 and 7 May 2020. In this period, the effective reproduction number is estimated with a minimum value of 0.18 and a maximum value of 1.78. Most importantly, the R(t) is strictly greater than one from April 13 till 7 May 2020. The R_0 is estimated to be 2.42 with credible interval: (2.37, 2.47). Comparing this with the R(t) shows that control measures are working but not effective enough to keep R(t) below one. Also, the estimated fractional reported symptomatic cases are between 10 to 50%. Our analysis has shown evidence that the existing control measures are not enough to end the epidemic and more stringent measures are needed.

scholarly journals Modeling the role of clusters and diffusion in the evolution of COVID-19 infections during lock-down

2020 ◽  
Author(s):  
W. J. T. Bos ◽  
J.-P. Bertoglio ◽  
L. Gostiaux
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Sir Model ◽  
Compartmental Models ◽  
European Countries ◽  
Epidemic Spreading ◽  
Decay Exponent ◽  
Local Reproduction ◽  
And Diffusion

Epidemics such as the spreading of the SARS-CoV-2 virus are highly non linear, and therefore difficult to predict. In the present pandemic as time evolves, it appears more and more clearly that a clustered dynamics is a key element of description. This means that the disease rapidly evolves within spatially localized networks, that diffuse and eventually create new clusters. We improve upon the simplest possible compartmental model, the SIR model, by adding an additional compartment associated with the clustered individuals. This sophistication is compatible with more advanced compartmental models and allows, at the lowest level of complexity, to leverage the well-mixedness assumption. The so-obtained SBIR model takes into account the effect of inhomogeneity on epidemic spreading, and compares satisfactorily with results on the pandemic propagation in a number of European countries, during and immediately after lock-down. Especially, the decay exponent of the number of new cases after the first peak of the epidemic is captured without the need to vary the coefficients of the model with time. We show that this decay exponent is directly determined by the diffusion of the ensemble of clustered individuals and can be related to a global reproduction number, that overrides the classical, local reproduction number.

SIR Model for Estimations of the Coronavirus Epidemic Dynamics in Iran

2020 ◽  
Author(s):  
Maryam Deldar ◽  
Samaneh Tahmasebi Ghorabi ◽  
Kourosh Sayehmiri
Keyword(s):  
Software Package ◽  
Sir Model ◽  
Global Model ◽  
Control Measures ◽  
The Novel ◽  
Timely Manner ◽  
Epidemic Disease ◽  
Epidemic Dynamics ◽  
Novel Coronavirus ◽  
Better Than

Background: The Coronavirus 2019-nCOV (COVID-19) epidemic by SARS-CoV-2 is spreading worldwide, and by March 1, 2020, 67 countries, including Iran, have been affected. Many studies are being conducted at home and abroad to predict the outbreak of the disease so that they can make the necessary medical and health decisions in a timely manner.  Methods: we used the SIR model to identify parameters to calculate epidemic features and some estimates of the new coronavirus. Data on the transmission of the novel coronavirus were extracted from the GitHub source in the covid19.analytics software package. Results: According to our model estimates, the rate of infection β = 1 and the rate of removal γ = 0.667 and index R0 = 1.497 were obtained. Because the value of R0 is more than one, it is still an epidemic disease. Given that tfinal~132 days was estimated, we can expect the transmission of this epidemic to stop in Iran after July 3, 2020, provided that existing quarantine measures and patient isolation rates continue as usual. In comparison with the global SIR model, we reached the peak of the infection earlierthan the global model, but in improved and susceptible cases, we performed better than the global model. The graph of recovered and susceptible cases in Iran earlier than the global model cut off themselves. Conclusion: Forecasts are set to be a useful guide for deciding whether to transfer COVID-19. According to the predictions and estimates made, more attention should be paid to control measures

scholarly journals Comparison of Numerical Simulation of Epidemiological Model between Euler Method with 4th Order Runge Kutta Method

2021 ◽  
Vol 2 (1) ◽  
pp. 37-44
Author(s):  
Rizky Ashgi
Keyword(s):  
Numerical Simulation ◽  
Numerical Methods ◽  
Sir Model ◽  
Euler Method ◽  
Kutta Method ◽  
System Of Differential Equations ◽  
Runge Kutta Method ◽  
Global Pandemic ◽  
The World ◽  
Runge Kutta

Coronavirus Disease 2019 has become global pandemic in the world. Since its appearance, many researchers in world try to understand the disease, including mathematics researchers. In mathematics, many approaches are developed to study the disease. One of them is to understand the spreading of the disease by constructing an epidemiology model. In this approach, a system of differential equations is formed to understand the spread of the disease from a population. This is achieved by using the SIR model to solve the system, two numerical methods are used, namely Euler Method and 4th order Runge-Kutta. In this paper, we study the performance and comparison of both methods in solving the model. The result in this paper that in the running process of solving it turns out that using the euler method is faster than using the 4th order Runge-Kutta method and the differences of solutions between the two methods are large.

scholarly journals A model for COVID-19 with isolation, quarantine and testing as control measures

2020 ◽  
Author(s):  
M.S. Aronna ◽  
R. Guglielmi ◽  
L.M. Moschen
Keyword(s):  
Compartmental Model ◽  
Reproduction Number ◽  
Risk Groups ◽  
Control Measures ◽  
Contact Rate ◽  
Control Parameters ◽  
Social Distancing ◽  
Proposed Model ◽  
Asymptomatic Infections ◽  
The Basic Reproduction Number

AbstractIn this article we propose a compartmental model for the dynamics of Coronavirus Disease 2019 (COVID-19). We take into account the presence of asymptomatic infections and the main policies that have been adopted so far to contain the epidemic: isolation (or social distancing) of a portion of the population, quarantine for confirmed cases and testing. We model isolation by separating the population in two groups: one composed by key-workers that keep working during the pandemic and have a usual contact rate, and a second group consisting of people that are enforced/recommended to stay at home. We refer to quarantine as strict isolation, and it is applied to confirmed infected cases.In the proposed model, the proportion of people in isolation, the level of contact reduction and the testing rate are control parameters that can vary in time, representing policies that evolve in different stages. We obtain an explicit expression for the basic reproduction number in terms of the parameters of the disease and of the control policies. In this way we can quantify the effect that isolation and testing have in the evolution of the epidemic. We present a series of simulations to illustrate different realistic scenarios. From the expression of and the simulations we conclude that isolation (social distancing) and testing among asymptomatic cases are fundamental actions to control the epidemic, and the stricter these measures are and the sooner they are implemented, the more lives can be saved. Additionally, we show that people that remain in isolation significantly reduce their probability of contagion, so risk groups should be recommended to maintain a low contact rate during the course of the epidemic.

MATHEMATICAL STUDY OF THE IMPACT OF QUARANTINE, ISOLATION AND VACCINATION IN CURTAILING AN EPIDEMIC

2007 ◽  
Vol 15 (02) ◽  
pp. 185-202 ◽  
Author(s):  
CHANDRA N. PODDER ◽  
ABBA B. GUMEL ◽  
CHRIS S. BOWMAN ◽  
ROBERT G. MCLEOD
Keyword(s):  
Disease Burden ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Control Measures ◽  
Vaccination Program ◽  
Reproductive Number ◽  
Mathematical Study ◽  
Asymptomatic Individuals ◽  
Combined Impact ◽  
The Impact

The quarantine of suspected cases and isolation of individuals with symptoms are two of the primary public health control measures for combating the spread of a communicable emerging or re-emerging disease. Implementing these measures, however, can inflict significant socio-economic and psychological costs. This paper presents a deterministic compartmental model for assessing the single and combined impact of quarantine and isolation to contain an epidemic. Comparisons are made with a mass vaccination program. The model is simulated using parameters for influenza-type diseases such as SARS. The study shows that even for an epidemic in which asymptomatic transmission does not occur, the quarantine of asymptomatically-infected individuals can be more effective than only isolating individuals with symptoms, if the associated reproductive number is high enough. For the case where asymptomatic transmission occurs, it is shown that isolation is more effective for a disease with a small basic reproduction number and transmission coefficient of asymptomatically-infected individuals. If asymptomatic individuals transmit at a rate that is at least 20% that of symptomatic individuals, quarantine is always more effective. The study further shows that the reduction in disease burden obtained from a combined quarantine and isolation program can be comparable to that obtained by a vaccination program, if the former is implemented quickly enough after the onset of the outbreak. If the implementation of such a quarantine/isolation program is delayed, however, even for a short while, its effectiveness decreases rapidly.

scholarly journals Mobility data can explain the entire COVID-19 outbreak course in Japan

2020 ◽  
Author(s):  
Junko Kurita ◽  
Tamie Sugawara ◽  
Yasushi Ohkusa
Keyword(s):  
Confidence Interval ◽  
Polynomial Function ◽  
Reproduction Number ◽  
Sir Model ◽  
Control Measures ◽  
Recovery Model ◽  
Mobility Data

AbstractBackgroundIn Japan, as a countermeasure against the COVID-19 outbreak, voluntary restrictions against going out (VRG) have been applied.ObjectWe examined mobility information provided by Apple Inc. to a susceptible–infected–recovery model.MethodWhen applying a polynomial function to daily Apple data with the SIR model, we presumed the function up to a cubic term as in our earlier study.ResultsEstimation results demonstrated R0 as 1.507 and its 95% confidence interval was [1.502, 1.509].. The estimated coefficients of Apple data was 1.748 and its 95% confidence interval was [1.731, 1.788].Discussion and ConclusionResults show that mobility data from Apple Inc. can explain the entire course of the outbreak in COVID-19 in Japan. Therefore, monitoring Apple data might be sufficient to adjust control measures to maintain an effective reproduction number of less than one.

scholarly journals Is Nigeria really on top of COVID-19? Message from effective reproduction number

2020 ◽  
Vol 148 ◽  
Author(s):  
A. I. Adekunle ◽  
O. A. Adegboye ◽  
E. Gayawan ◽  
E. S. McBryde
Keyword(s):  
Public Health ◽  
Compartmental Model ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Credible Interval ◽  
Control Measures ◽  
Maximum Value ◽  
Intervention Measures ◽  
Death Cases ◽  
Epidemiological Parameters

Abstract Following the importation of coronavirus disease (COVID-19) into Nigeria on 27 February 2020 and then the outbreak, the question is: How do we anticipate the progression of the ongoing epidemic following all the intervention measures put in place? This kind of question is appropriate for public health responses and it will depend on the early estimates of the key epidemiological parameters of the virus in a defined population. In this study, we combined a likelihood-based method using a Bayesian framework and compartmental model of the epidemic of COVID-19 in Nigeria to estimate the effective reproduction number (R(t)) and basic reproduction number (R0) – this also enables us to estimate the initial daily transmission rate (β0). We further estimate the reported fraction of symptomatic cases. The models are applied to the NCDC data on COVID-19 symptomatic and death cases from 27 February 2020 and 7 May 2020. In this period, the effective reproduction number is estimated with a minimum value of 0.18 and a maximum value of 2.29. Most importantly, the R(t) is strictly greater than one from 13 April till 7 May 2020. The R0 is estimated to be 2.42 with credible interval: (2.37–2.47). Comparing this with the R(t) shows that control measures are working but not effective enough to keep R(t) below 1. Also, the estimated fraction of reported symptomatic cases is between 10 and 50%. Our analysis has shown evidence that the existing control measures are not enough to end the epidemic and more stringent measures are needed.

scholarly journals A Discrete Numerical Solution of The SIR Model with Horizontal and Vertical Transmission

CAUCHY ◽  
2019 ◽  
Vol 6 (1) ◽  
pp. 1
Author(s):  
Trija Fayeldi
Keyword(s):  
Numerical Solution ◽  
Vertical Transmission ◽  
Reproduction Number ◽  
Equilibrium Points ◽  
Sir Model ◽  
Euler Method ◽  
Discrete Version ◽  
Step Size ◽  
The Stability ◽  
Disease Free

The aim of this paper is to is to generalize the SIR model with horizontal and vertical transmission. In this paper, we develop the discrete version of the model. We use Euler method to approximate numerical solution of the model. We found two equilibrium points, that is disease free and endemic equilibrium points. The existence of these points depend on basic reproduction number <em>R</em><sub>0</sub>. We found that if <em>R</em><sub>0</sub> <span style="text-decoration-line: underline;">&lt;</span> 1 then only disease free equilibrium points exists, while both points exists when <em>R</em><sub>0</sub> &gt; 1. We also found that the stability of these equilibrium points depend on the value of step-size <em>h</em>. Some numerical experiments were presented as illustration.

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