Describing the COVID-19 outbreak during the lockdown: fitting modified SIR models to data

Ianni, Aldo; Rossi, N.

doi:10.1140/epjp/s13360-020-00895-7

Cited by 20 publications

(19 citation statements)

References 11 publications

(11 reference statements)

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“…SIRD (Susceptible, Infectious, Recovered, and Dead) is a four-compartment model that has been widely used as a forecasting method of infectious disease [ 1 – 4 , 16 , 17 , 22 , 34 ]. In the SIRD model, the number of susceptible individuals ( S ), infected individuals ( I ), recovered individuals ( R ), and dead individuals ( D ) vary with time ( t ) as follows [ 2 , 16 , 17 ]: where β is the transmission rate (infection), γ is the recovery rate, and δ is the death rate.…”

Section: Methodsmentioning

confidence: 99%

“…However, fewer individuals of size S are susceptible through control measures such as restriction of movements, self-isolation, and social distancing [ 31 , 32 ]. While the initial number of susceptible individuals, S (0), is required for inverse modelling, estimating the actual population size under study can be challenging [ 31 , 33 , 34 ]. In the recent studies considering inverse COVID-19 modelling, several assumptions or methods were used to choose the total population size, N .…”

Section: Introductionmentioning

confidence: 99%

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An application of the ensemble Kalman filter in epidemiological modelling

Lal

Huang

2021

PLoS ONE

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Since the novel coronavirus (COVID-19) outbreak in China, and due to the open accessibility of COVID-19 data, several researchers and modellers revisited the classical epidemiological models to evaluate their practical applicability. While mathematical compartmental models can predict various contagious viruses’ dynamics, their efficiency depends on the model parameters. Recently, several parameter estimation methods have been proposed for different models. In this study, we evaluated the Ensemble Kalman filter’s performance (EnKF) in the estimation of time-varying model parameters with synthetic data and the real COVID-19 data of Hubei province, China. Contrary to the previous works, in the current study, the effect of damping factors on an augmented EnKF is studied. An augmented EnKF algorithm is provided, and we present how the filter performs in estimating models using uncertain observational (reported) data. Results obtained confirm that the augumented-EnKF approach can provide reliable model parameter estimates. Additionally, there was a good fit of profiles between model simulation and the reported COVID-19 data confirming the possibility of using the augmented-EnKF approach for reliable model parameter estimation.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An application of the ensemble Kalman filter in epidemiological modelling

Lal

Huang

2021

PLoS ONE

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“…A deterministic model based on SIR framework was proposed to understand the evolution of COVID-19 outbreaks during lockdown and social distancing policy in Germany and Italy by Ianni and Rossi [ 57 ]. Similarly, Köhler-Rieper et al [ 58 ] proposed a new approach to mathematical modelling of COVID-19 transmission dynamics by constructing a single ordinary integro-differential equation.…”

Section: Introductionmentioning

confidence: 99%

Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study

Abidemi

Zainuddin²,

Aziz³

2021

Eur. Phys. J. Plus

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Coronavirus disease 2019 (COVID-19) pandemic has posed a serious threat to both the human health and economy of the affected nations. Despite several control efforts invested in breaking the transmission chain of the disease, there is a rise in the number of reported infected and death cases around the world. Hence, there is the need for a mathematical model that can reliably describe the real nature of the transmission behaviour and control of the disease. This study presents an appropriately developed deterministic compartmental model to investigate the effect of different pharmaceutical (treatment therapies) and non-pharmaceutical (particularly, human personal protection and contact tracing and testing on the exposed individuals) control measures on COVID-19 population dynamics in Malaysia. The data from daily reported cases of COVID-19 between 3 March and 31 December 2020 are used to parameterize the model. The basic reproduction number of the model is estimated. Numerical simulations are carried out to demonstrate the effect of various control combination strategies involving the use of personal protection, contact tracing and testing, and treatment control measures on the disease spread. Numerical simulations reveal that the implementation of each strategy analysed can significantly reduce COVID-19 incidence and prevalence in the population. However, the results of effectiveness analysis suggest that a strategy that combines both the pharmaceutical and non-pharmaceutical control measures averts the highest number of infections in the population.

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“…The authors also used numerical method namely Runge–Kutta method for numerically solving the model. In [ 32 ] and [ 33 ], authors did a study based on disease outbreak during lockdown in Italy and attainment of herd immunity in India, respectively. In the former work, the authors fitted both daily new cases as well as a total of the diseased and recovered cases.…”

Section: Introductionmentioning

confidence: 99%

Modeling of COVID-19 with limited public health resources: a comparative study of three most affected countries

2021

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COVID-19 has become a deadly pandemic in the recent times claiming millions of lives worldwide in a grievous manner. Most of the countries in the world have limited number of medical resources (hospitals, beds, ventilators, etc.), and in the case of large outbreak, it becomes very difficult to provide treatment to every infected individual. In this study, we propound a mathematical model where we classify the infected into two subcategories—asymptomatic and symptomatic. This model further accounts for the effect of limited medical resource for infected people and using face masks in combating the pandemic. Focusing on these aspects, we analyze the model and exploit the available data for assessing the pattern in three most affected countries, namely USA, India and Brazil. The developed model is calibrated to fit data for these three countries and estimate the transmission rate of symptomatic, asymptomatic individuals. The rate at which the individuals who are quarantined recover is estimated as well. Along with these estimations, a comparative study based on the basic reproduction number estimated for the three countries is presented. Standard methods of sensitivity analysis are performed to analyze the ways in which basic reproduction number is impacted upon due to changes in different parameters of the model. Further, we obtain disease-free equilibrium and endemic equilibrium of the model. It is observed that backward bifurcation occurs if the capacity of treatment is small and bistable equilibria are shown that makes the system more sensitive to the initial conditions. Sufficient conditions for the local asymptomatic stability of the endemic equilibrium and disease-free equilibrium of the system are obtained. The results of this study imply that to curb the severity of the increasing cases of the disease in these countries, effective strategies to control disease spread should be implemented so that the basic reproduction number can be decreased below the threshold value which is certainly less than unity. The use of protective masks in public is shown to be an important preventive measure to lower disease transmission rate. Also, the quantity of medical resources should increase so that every infected person can get better treatment.

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Describing the COVID-19 outbreak during the lockdown: fitting modified SIR models to data

Cited by 20 publications

References 11 publications

An application of the ensemble Kalman filter in epidemiological modelling

An application of the ensemble Kalman filter in epidemiological modelling

Impact of control interventions on COVID-19 population dynamics in Malaysia: a mathematical study

Modeling of COVID-19 with limited public health resources: a comparative study of three most affected countries

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