Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America

Marinovg, Tchavdar T.; Marinova, Rossitza S.

doi:10.1016/j.idm.2021.12.001

Cited by 17 publications

(14 citation statements)

References 28 publications

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“…The number of cases of people recovered from COVID-19 who are re-infected at the present moment is very limited, and the rate cannot be estimated; thus, the possibility of reinfection is not taken into account. Specific details on the assumptions and the adaptive SIR (A-SIR) model can be found in [ 40 , 41 ].…”

Section: The Sir Model For the Spread Of An Infectious Diseasementioning

confidence: 99%

“…The present work proposes a novel approach for the identification of the time-dependent reproduction numbers. It extends the SIR-type model by assuming time-dependent infection and recovery rates [ 40 , 41 ], which are required for the estimation of the reproduction numbers. The method is based on direct integration of the SIR system and an inverse problem approach for solving the resulting equation for the ratio of the infection and recovery rates.…”

Section: Introductionmentioning

confidence: 99%

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Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

Marinov,

Marinova,

Marinov

et al. 2023

Viruses

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This paper presents a novel numerical technique for the identification of effective and basic reproduction numbers, Re and R0, for long-term epidemics, using an inverse problem approach. The method is based on the direct integration of the SIR (Susceptible–Infectious–Removed) system of ordinary differential equations and the least-squares method. Simulations were conducted using official COVID-19 data for the United States and Canada, and for the states of Georgia, Texas, and Louisiana, for a period of two years and ten months. The results demonstrate the applicability of the method in simulating the dynamics of the epidemic and reveal an interesting relationship between the number of currently infectious individuals and the effective reproduction number, which is a useful tool for predicting the epidemic dynamics. For all conducted experiments, the results show that the local maximum (and minimum) values of the time-dependent effective reproduction number occur approximately three weeks before the local maximum (and minimum) values of the number of currently infectious individuals. This work provides a novel and efficient approach for the identification of time-dependent epidemics parameters.

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Section: The Sir Model For the Spread Of An Infectious Diseasementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

Marinov,

Marinova,

Marinov

et al. 2023

Viruses

Self Cite

View full text Add to dashboard Cite

show abstract

“…The Euler method uses its slope at a point to find the numerical solution near that point. In contrast, the R-K method is the extension modification of the Euler method, which has a higher level of accuracy [ 25 – 28 ]. Therefore, we have adopted this method for our study, compared the obtained results, and drew conclusions based on the outcomes.…”

Section: Introductionmentioning

confidence: 99%

Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel

Verma

Tiwari

Verma

2023

Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci.

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This study presents a fractional-order mathematical model of coronavirus. We select COVID-19 model and convert the model into fractional order. Discuss its theoretical and numerical analysis. Firstly, we investigate the existence and uniqueness results using some fixed point theorems for the proposed fractional-order COVID-19 model. Further, we provide the stability analysis with the help of the Hyers-Ulam stability. The fractional operator is used in the Caputo sense. We obtain numerical solutions using famous numerical methods and provide a graphical interpretation using adopted numerical methods. Finally, we compare the above techniques and provide observations according to the obtained solutions.

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“…This is very useful for public health and preventive healthcare. For this 5 reason, in efforts to prevent the COVID-19 epidemic, many mathematicians and epidemiologists have proposed and analyzed a great number of mathematical models describing transmission dynamics of the COVID-19 (see, for example, [6,22,33,34,39,40,49,50,51,54,59,60] and references therein). As an important consequence, mitigation and prevention measures of COVID-19 outbreaks were suggested.…”

Section: Introductionmentioning

confidence: 99%

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

Hoang

2023

Preprint

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Although Coronavirus disease 2019 (COVID-19) pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been controlled and prevented, mathematical modeling and analysis of transmission dynamics of COVID-19 still plays an essential role not only in the post COVID-19 era but also in the study of infectious diseases. This is an important foundation to propose effective strategies and measures for controlling diseases and projecting public health. This work is devoted to proposing and analyzing a new mathematical study for transmission dynamics of COVID-19. We first introduce a generalized SEIR epidemic model that use general nonlinear incidence rates to describe the “psychological” effect. After that, a rigorous mathematical analysis for the proposed COVID-19 model is performed. We establish the positivity and boundedness, calculate the basic reproduction number, determine possible (disease-free and endemic-disease) equilibrium points and investigate their asymptotic stability properties of the SEIR model. The obtained results improve and extend an SEIR model constructed in a recent work. For the purpose of numerical simulation, the Mickens’ methodology is applied to construct a dynamically consistent nonstandard finite difference (NSFD) model for the proposed SEIR epidemic model. The constructed NSFD scheme has the ability to provide reliable approximations that not only preserve the dynamical properties of the SEIR model for all the values of the step size but also are easy to be implemented. Finally, a set of illustrative numerical experiments is conducted to support the theoretical findings and to confirm advantages of the NSFD scheme over some well-known standard ones.

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Inverse problem for adaptive SIR model: Application to COVID-19 in Latin America

Cited by 17 publications

References 28 publications

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

Novel Approach for Identification of Basic and Effective Reproduction Numbers Illustrated with COVID-19

Theoretical and Numerical Analysis of Fractional Order Mathematical Model on Recent COVID-19 Model Using Singular Kernel

A dynamically consistent nonstandard finite difference scheme for a generalized SEIR epidemic model

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