COVID-19 Epidemic Forecast in Different States of India using SIR Model

The epidemiological data up to 12th May 2020 for India and its 24 states has been used to predict COVID-19 outbreak within classical SIR (Susceptible-Infected-Recovered) model. The basic reproduction number R0 of India is calculated to be 1.15, whereas for various states it ranges from 1.03 in Uttarakhand to 7.92 in Bihar. The statistical parameters for most of the states indicates the high significance of the predicted results. It is estimated that the epidemic curve flattening in India will start from the first week of July and epidemic may end in the third week of October with final epidemic size ~1,75,000. The epidemic in Kerala is in final phase and is expected to end by first week of June. Among Indian states, Maharashtra is severely affected where the ending phase of epidemic may occur in the second week of September with epidemic size of ~55,000. The model indicates that the fast growth of infection in Punjab is from 27th April 2020 to 2nd June 2020, thereafter, curve flattening will start and the epidemic is expected to finished by the first week of July with the estimated number of ~3300 infected people. The epidemic size of COVID-19 outbreak in Delhi, West Bengal, Gujrat, Tamil Nadu and Odisha can reach as large as 24,000, 18,000, 16,000, 13,000 and 11,000, respectively, however, these estimations may be invalid if large fluctuation of data occurs in coming days.

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Optimal timing for social distancing during an epidemic

10.1101/2020.03.30.20048132 ◽

2020 ◽

Cited By ~ 1

Author(s):

Oscar Patterson-Lomba

Keyword(s):

Reproduction Number ◽

Decision Makers ◽

Optimal Time ◽

Optimal Timing ◽

Epidemiological Models ◽

Pharmacological Interventions ◽

Social Distancing ◽

Epidemic Curve ◽

Epidemic Size ◽

Final Epidemic Size

AbstractSocial distancing is an effective way to contain the spread of a contagious disease, particularly when facing a novel pathogen and no pharmacological interventions are available. In such cases, conventional wisdom suggests that social distancing measures should be introduced as soon as possible after the beginning of an outbreak to more effectively mitigate the spread of the disease. Using a simple epidemiological model we show that, however, there is in fact an optimal time to initiate a temporal social distancing intervention if the goal is to reduce the final epidemic size or “flatten” the epidemic curve. The optimal timing depends strongly on the effective reproduction number (R0) of the disease, such that as the R0 increases, the optimal time decreases non-linearly. Additionally, if pharmacological interventions (e.g., a vaccine) become available at some point during the epidemic, the sooner these interventions become available the sooner social distancing should be initiated to maximize its effectiveness. Although based on a simple model, we hope that these insights inspire further investigations within the context of more complex and data-driven epidemiological models, and can ultimately help decision makers to improve temporal social distancing policies to mitigate the spread of epidemics.

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Assessing the impact of adherence to Non-pharmaceutical interventions and indirect transmission on the dynamics of COVID-19: a mathematical modelling study

10.1101/2021.08.16.21262135 ◽

2021 ◽

Author(s):

Sarafa A. Iyaniwura ◽

Musa Rabiu ◽

Jummy F. David ◽

Jude D. Kong

Keyword(s):

Public Health ◽

Reproduction Number ◽

Health Policies ◽

Public Health Policies ◽

Indirect Transmission ◽

Epidemic Size ◽

Final Epidemic Size ◽

The Impact ◽

Size Relation ◽

Pharmaceutical Interventions

AbstractAdherence to public health policies such as the non-pharmaceutical interventions implemented against COVID-19 plays a major role in reducing infections and controlling the spread of the diseases. In addition, understanding the transmission dynamics of the disease is also important in order to make and implement efficient public health policies. In this paper, we developed an SEIR-type compartmental model to assess the impact of adherence to COVID-19 non-pharmaceutical interventions and indirect transmission on the dynamics of the disease. Our model considers both direct and indirect transmission routes and stratifies the population into two groups: those that adhere to COVID-19 non-pharmaceutical interventions (NPIs) and those that do not adhere to the NPIs. We compute the control reproduction number and the final epidemic size relation for our model and study the effect of different parameters of the model on these quantities. Our results show that direct transmission has more effect on the reproduction number and final epidemic size, relative to indirect transmission. In addition, we showed that there is a significant benefit in adhering to the COVID-19 NPIs.

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Prediction of the Epidemic Peak of Coronavirus Disease in Japan, 2020

Journal of Clinical Medicine ◽

10.3390/jcm9030789 ◽

2020 ◽

Vol 9 (3) ◽

pp. 789 ◽

Cited By ~ 74

Author(s):

Toshikazu Kuniya

Keyword(s):

Compartmental Model ◽

Reproduction Number ◽

Least Square ◽

Time Data ◽

Long Period ◽

Epidemic Size ◽

First Case ◽

Final Epidemic Size ◽

Positive Effect ◽

Day By Day

The first case of coronavirus disease 2019 (COVID-19) in Japan was reported on 15 January 2020 and the number of reported cases has increased day by day. The purpose of this study is to give a prediction of the epidemic peak for COVID-19 in Japan by using the real-time data from 15 January to 29 February 2020. Taking into account the uncertainty due to the incomplete identification of infective population, we apply the well-known SEIR compartmental model for the prediction. By using a least-square-based method with Poisson noise, we estimate that the basic reproduction number for the epidemic in Japan is R 0 = 2.6 ( 95 % CI, 2.4 – 2.8 ) and the epidemic peak could possibly reach the early-middle summer. In addition, we obtain the following epidemiological insights: (1) the essential epidemic size is less likely to be affected by the rate of identification of the actual infective population; (2) the intervention has a positive effect on the delay of the epidemic peak; (3) intervention over a relatively long period is needed to effectively reduce the final epidemic size.

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Implementation of An Online COVID-19 Epidemic Calculator for Tracking the Spread of the Coronavirus in Singapore and Other Countries

10.1101/2020.06.02.20120188 ◽

2020 ◽

Author(s):

Fook Fah Yap ◽

Minglee Yong

Keyword(s):

Doubling Time ◽

Reproduction Number ◽

Growth Parameters ◽

Circuit Breaker ◽

The Public ◽

Slowing Down ◽

Epidemic Size ◽

Final Epidemic Size ◽

Case Data

AbstractThis paper describes the methods underlying the development of an online COVID-19 Epidemic Calculator for tracking COVID-19 growth parameters. From publicly available infection case data, the calculator is used to estimate the effective reproduction number, doubling time, final epidemic size, and death toll. As a case study, we analyzed the results for Singapore during the “Circuit breaker” period from April 7, 2020 to the end of May 2020. The calculator shows that the stringent measures imposed have an immediate effect of rapidly slowing down the spread of the coronavirus. After about two weeks, the effective reproduction number reduced to 1.0. Since then, the number has been fluctuating around 1.0.The COVID-19 Epidemic Calculator is available in the form of an online Google Sheet and the results are presented as Tableau Public dashboards at www.cv19.one. By making the calculator readily accessible online, the public can have a tool to meaningfully assess the effectiveness of measures to control the pandemic.

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Temporal evolution of COVID-19 in the states of India using SIQR Model

10.1101/2020.06.08.20125658 ◽

2020 ◽

Cited By ~ 1

Author(s):

Alok Tiwari

Keyword(s):

Tamil Nadu ◽

Temporal Evolution ◽

Reproduction Number ◽

Uttar Pradesh ◽

National Average ◽

Indian Government ◽

Indian States ◽

Steady Rate ◽

Entire Nation ◽

Second Wave

ABSTRACTCOVID 19 entered during the last week of April 2020 in India has caused 3,546 deaths with 1,13,321 number of reported cases. Indian government has taken many proactive steps, including strict lockdown of the entire nation for more than 50 days, identification of hotspots, app-based tracking of citizens to track infected. This paper investigated the evolution of COVID 19 in five states of India (Maharashtra, UP, Gujrat, Tamil Nadu, and Delhi) from 1st April 2020 to 20th May 2020. Variation of doubling rate and reproduction number (from SIQR) with time is used to analyse the performance of the majorly affected Indian states. It has been determined that Uttar Pradesh is one of the best performers among five states with the doubling rate crossing 18 days as of 20th May. Tamil Nadu has witnessed the second wave of infections during the second week of May. Maharashtra is continuously improving at a steady rate with its doubling rate reaching to 12.67 days. Also these two states are performing below the national average in terms of infection doubling rate. Gujrat and Delhi have reported the doubling rate of 16.42 days and 15.49 days respectively. Comparison of these states has also been performed based on time-dependent reproduction number. Recovery rate of India has reached to 40 % as the day paper is written.

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Pairwise approximation for SIR -type network epidemics with non-Markovian recovery

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2017.0695 ◽

2018 ◽

Vol 474 (2210) ◽

pp. 20170695 ◽

Cited By ~ 4

Author(s):

G. Röst ◽

Z. Vizi ◽

I. Z. Kiss

Keyword(s):

Recovery Time ◽

Reproduction Number ◽

Mean Field ◽

Stochastic Network ◽

Hyperbolic Partial Differential Equation ◽

Epidemic Size ◽

Major Benefit ◽

Pairwise Models ◽

Final Epidemic Size ◽

Pairwise Model

We present the generalized mean-field and pairwise models for non-Markovian epidemics on networks with arbitrary recovery time distributions. First we consider a hyperbolic partial differential equation (PDE) system, where the population of infective nodes and links are structured by age since infection. We show that the PDE system can be reduced to a system of integro-differential equations, which is analysed analytically and numerically. We investigate the asymptotic behaviour of the generalized model and provide an implicit analytical expression involving the final epidemic size and pairwise reproduction number. As an illustration of the applicability of the general model, we recover known results for the exponentially distributed and fixed recovery time cases. For gamma- and uniformly distributed infectious periods, new pairwise models are derived. Theoretical findings are confirmed by comparing results from the new pairwise model and explicit stochastic network simulation. A major benefit of the generalized pairwise model lies in approximating the time evolution of the epidemic.

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Regression Analysis of COVID-19 Spread in India and its Different States

10.1101/2020.05.29.20117069 ◽

2020 ◽

Cited By ~ 3

Author(s):

Poonam Chauhan ◽

Ashok Kumar ◽

Pooja Jamdagni

Keyword(s):

Regression Analysis ◽

Regression Model ◽

Tamil Nadu ◽

Polynomial Regression ◽

Case Fatality ◽

Epidemiological Data ◽

Fatality Rate ◽

Indian States ◽

Number Of Patients ◽

Polynomial Regression Model

AbstractLinear and polynomial regression model has been used to investigate the COVID-19 outbreak in India and its different states using time series epidemiological data up to 26th May 2020. The data driven analysis shows that the case fatality rate (CFR) for India (3.14% with 95% confidence interval of 3.12% to 3.16%) is half of the global fatality rate, while higher than the CFR of the immediate neighbors i.e. Bangladesh, Pakistan and Sri Lanka. Among Indian states, CFR of West Bengal (8.70%, CI: 8.21–9.18%) and Gujrat (6.05%, CI: 4.90–7.19%) is estimated to be higher than national rate, whereas CFR of Bihar, Odisha and Tamil Nadu is less than 1%. The polynomial regression model for India and its different states is trained with data from 21st March 2020 to 19th May 2020 (60 days). The performance of the model is estimated using test data of 7 days from 20th May 2020 to 26th May 2020 by calculating RMSE and % error. The model is then used to predict number of patients in India and its different states up to 16th June 2020 (21 days). Based on the polynomial regression analysis, Maharashtra, Gujrat, Delhi and Tamil Nadu are continue to remain most affected states in India.

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Dynamical analysis in disease transmission and final epidemic size

Communications on Pure and Applied Analysis ◽

10.3934/cpaa.2021150 ◽

2021 ◽

Vol 0 (0) ◽

pp. 0

Author(s):

Daifeng Duan ◽

Cuiping Wang ◽

Yuan Yuan

Keyword(s):

Basic Reproduction Number ◽

Disease Transmission ◽

Reproduction Number ◽

Dynamical Analysis ◽

Health Care Demand ◽

Future Health ◽

Epidemic Size ◽

Future Health Care ◽

Final Epidemic Size ◽

The Basic Reproduction Number

<p style='text-indent:20px;'>We propose two compartment models to study the disease transmission dynamics, then apply the models to the current COVID-19 pandemic and to explore the potential impact of the interventions, and try to provide insights into the future health care demand. Starting with an SEAIQR model by combining the effect from exposure, asymptomatic and quarantine, then extending the model to the one with ages below and above 65 years old, and classify the infectious individuals according to their severity. We focus our analysis on each model with and without vital dynamics. In the models with vital dynamics, we study the dynamical properties including the global stability of the disease free equilibrium and the existence of endemic equilibrium, with respect to the basic reproduction number. Whereas in the models without vital dynamics, we address the final epidemic size rigorously, which is one of the common but difficult questions regarding an epidemic. Finally, we apply our models to estimate the basic reproduction number and the final epidemic size of disease by using the data of COVID-19 confirmed cases in Canada and Newfoundland & Labrador province.</p>

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Temporal evolution of COVID-19 in the states of India using SIQR Model (Preprint)

10.2196/preprints.21284 ◽

2020 ◽

Author(s):

Alok Tiwari

Keyword(s):

Tamil Nadu ◽

Temporal Evolution ◽

Reproduction Number ◽

Uttar Pradesh ◽

National Average ◽

Indian Government ◽

Indian States ◽

Steady Rate ◽

Second Wave ◽

Second Peak

BACKGROUND COVID 19 entered during the last week of April 2020 in India has caused 3,546 deaths with 1,13,321 number of reported cases. Indian government has taken many proactive steps, including strict lockdown of the entire nation for more than 50 days, identification of hotspots, app-based tracking of citizens to track infected. OBJECTIVE This paper investigated the evolution of COVID 19 in five states of India (Maharashtra, UP, Gujrat, Tamil Nadu, and Delhi) from 1st April 2020 to 20th May 2020 METHODS Variation of doubling rate and reproduction number (from SIQR) with time is used to analyse the performance of the majorly affected Indian states RESULTS . It has been determined that Uttar Pradesh is one of the best performers among five states with the doubling rate crossing 18 days as of 20th May. Tamil Nadu has witnessed the second wave of infections during the second week of May. Maharashtra is continuously improving at a steady rate with its doubling rate reaching to 12.67 days. Also these two states are performing below the national average in terms of infection doubling rate. Gujrat and Delhi have reported the doubling rate of 16.42 days and 15.49 days respectively. Comparison of these states has also been performed based on time-dependent reproduction number. Recovery rate of India has reached to 40 % as the day paper is written. CONCLUSIONS All the three major contributing states of India as improving slowly. Tamil Nadu witnessed the second peak during mid of May, Maharasthra alongwith Tamil Nadu is performing below the national average. This kind of analysis can be useful for the analysis of evolution of COVID 19 among different states of India.

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Imported and autochthonous cases in the dynamics of dengue epidemics in Brazil

Revista de Saúde Pública ◽

10.1590/s0034-89102009000100001 ◽

2009 ◽

Vol 43 (1) ◽

pp. 1-7 ◽

Cited By ~ 15

Author(s):

Nicolas Degallier ◽

Charly Favier ◽

Jean-Philippe Boulanger ◽

Christophe Menkes

Keyword(s):

Basic Reproduction Number ◽

Reproduction Number ◽

Epidemiological Data ◽

Epidemic Curve ◽

Epidemic Dynamics ◽

Reproduction Numbers ◽

Imported Cases ◽

And Control ◽

Dengue Epidemic ◽

The Basic Reproduction Number

OBJECTIVE: To estimate the basic reproduction number (R0) of dengue fever including both imported and autochthonous cases. METHODS: The study was conducted based on epidemiological data of the 2003 dengue epidemic in Brasília, Brazil. The basic reproduction number is estimated from the epidemic curve, fitting linearly the increase of initial cases. Aiming at simulating an epidemic with both autochthonous and imported cases, a "susceptible-infectious-resistant" compartmental model was designed, in which the imported cases were considered as an external forcing. The ratio between R0 of imported versus autochthonous cases was used as an estimator of real R0. RESULTS: The comparison of both reproduction numbers (only autochthonous versus all cases) showed that considering all cases as autochthonous yielded a R0 above one, although the real R0 was below one. The same results were seen when the method was applied on simulated epidemics with fixed R0. This method was also compared to some previous proposed methods by other authors and showed that the latter underestimated R0 values. CONCLUSIONS: It was shown that the inclusion of both imported and autochthonous cases is crucial for the modeling of the epidemic dynamics, and thus provides critical information for decision makers in charge of prevention and control of this disease.

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