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  1. Article: Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity.

    Vyasarayani, C P / Chatterjee, Anindya

    Nonlinear dynamics

    2020  Volume 101, Issue 3, Page(s) 1653–1665

    Abstract: We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable ... ...

    Abstract We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities
    Keywords covid19
    Language English
    Publishing date 2020-07-11
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 2012600-1
    ISSN 1573-269X ; 0924-090X
    ISSN (online) 1573-269X
    ISSN 0924-090X
    DOI 10.1007/s11071-020-05785-2
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  2. Article: New approximations, and policy implications, from a delayed dynamic model of a fast pandemic.

    Vyasarayani, C P / Chatterjee, Anindya

    Physica D. Nonlinear phenomena

    2020  Volume 414, Page(s) 132701

    Abstract: We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model due to Young et al. (2019) for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone ... ...

    Abstract We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model due to Young et al. (2019) for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The simple subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave (short delay) approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how a well executed temporary phase of social distancing can reduce the total number of people affected. The reduction can be by as much as half for a weak pandemic, and is smaller but still substantial for stronger pandemics. An explicit formula for the greatest possible reduction is given.
    Keywords covid19
    Language English
    Publishing date 2020-08-25
    Publishing country Netherlands
    Document type Journal Article
    ZDB-ID 1466587-6
    ISSN 1872-8022 ; 0167-2789
    ISSN (online) 1872-8022
    ISSN 0167-2789
    DOI 10.1016/j.physd.2020.132701
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  3. Article ; Online: Author Correction: Data suggest COVID-19 affected numbers greatly exceeded detected numbers, in four European countries, as per a delayed SEIQR model.

    Tiwari, Sankalp / Vyasarayani, C P / Chatterjee, Anindya

    Scientific reports

    2021  Volume 11, Issue 1, Page(s) 11347

    Language English
    Publishing date 2021-05-25
    Publishing country England
    Document type Published Erratum
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-021-90076-y
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  4. Article ; Online: Data suggest COVID-19 affected numbers greatly exceeded detected numbers, in four European countries, as per a delayed SEIQR model.

    Tiwari, Sankalp / Vyasarayani, C P / Chatterjee, Anindya

    Scientific reports

    2021  Volume 11, Issue 1, Page(s) 8106

    Abstract: People in many countries are now infected with COVID-19. By now, it is clear that the number of people infected is much greater than the number of reported cases. To estimate the infected but undetected/unreported cases using a mathematical model, we can ...

    Abstract People in many countries are now infected with COVID-19. By now, it is clear that the number of people infected is much greater than the number of reported cases. To estimate the infected but undetected/unreported cases using a mathematical model, we can use a parameter called the probability of quarantining an infected individual. This parameter exists in the time-delayed SEIQR model (Scientific Reports, article number: 3505). Here, two limiting cases of a network of such models are used to estimate the undetected population. The first limit corresponds to the network collapsing onto a single node and is referred to as the mean-[Formula: see text] model. In the second case, the number of nodes in the network is infinite and results in a continuum model wherein the infectivity is statistically distributed. We use a generalized Pareto distribution to model the infectivity. This distribution has a fat tail and models the presence of super-spreaders that contribute to the disease progression. While both models capture the detected numbers well, the predictions of affected numbers from the continuum model are more realistic. Our results suggest that affected people outnumber detected people by one to two orders of magnitude in Spain, the UK, Italy, and Germany. Our results are consistent with corresponding trends obtained from published serological studies in Spain, the UK and Italy. The match with limited studies in Germany is poor, possibly because Germany's partial lockdown approach requires different modeling.
    MeSH term(s) COVID-19/diagnosis ; COVID-19/epidemiology ; Europe/epidemiology ; Humans ; Models, Theoretical ; Probability ; Quarantine
    Language English
    Publishing date 2021-04-14
    Publishing country England
    Document type Journal Article
    ZDB-ID 2615211-3
    ISSN 2045-2322 ; 2045-2322
    ISSN (online) 2045-2322
    ISSN 2045-2322
    DOI 10.1038/s41598-021-87630-z
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  5. Article: Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

    C. Vyasarayani P. / Anindya Chatterjee

    Abstract: We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity, and consider the continuum limit of the same with a simple separable ...

    Abstract We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity, and consider the continuum limit of the same with a simple separable interaction model for the infectivities $\\beta$. Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of $\\beta$ in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in $\\beta$ appears through an integral closely related to the moment generating function of $u=\\sqrt{\\beta}$. If the first few moments of $u$ exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single $\\beta$. Even otherwise, the new scalar DDE can be solved using either numerical integration over $u$ at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model, and will hopefully lead to new analysis of continuum models for epidemics.
    Keywords covid19
    Publisher arxiv
    Document type Article
    Database COVID19

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  6. Article: New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

    C. Vyasarayani P. / Anindya Chatterjee

    Abstract: We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, ...

    Abstract We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how correctly executed time-varying social distancing, within the present model, can cut the number of affected people by almost half. Alternatively, faster detection followed by near-certain quarantining can potentially be even more effective.
    Keywords covid19
    Publisher arxiv
    Document type Article
    Database COVID19

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  7. Article: Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

    Vyasarayani, C P / Chatterjee, Anindya

    Nonlinear Dyn

    Abstract: We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable ... ...

    Abstract We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity and consider the continuum limit of the same with a simple separable interaction model for the infectivities ß . Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of ß in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in ß appears through an integral closely related to the moment generating function of u = ß . If the first few moments of u exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single ß . Even otherwise, the new scalar DDE can be solved using either numerical integration over u at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model and will hopefully lead to new analysis of continuum models for epidemics.
    Keywords covid19
    Publisher WHO
    Document type Article
    Note WHO #Covidence: #638659
    Database COVID19

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  8. Book ; Online: Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity

    Vyasarayani, C. P. / Chatterjee, Anindya

    2020  

    Abstract: We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity, and consider the continuum limit of the same with a simple separable ...

    Abstract We take up a recently proposed compartmental SEIQR model with delays, ignore loss of immunity in the context of a fast pandemic, extend the model to a network structured on infectivity, and consider the continuum limit of the same with a simple separable interaction model for the infectivities $\beta$. Numerical simulations show that the evolving dynamics of the network is effectively captured by a single scalar function of time, regardless of the distribution of $\beta$ in the population. The continuum limit of the network model allows a simple derivation of the simpler model, which is a single scalar delay differential equation (DDE), wherein the variation in $\beta$ appears through an integral closely related to the moment generating function of $u=\sqrt{\beta}$. If the first few moments of $u$ exist, the governing DDE can be expanded in a series that shows a direct correspondence with the original compartmental DDE with a single $\beta$. Even otherwise, the new scalar DDE can be solved using either numerical integration over $u$ at each time step, or with the analytical integral if available in some useful form. Our work provides a new academic example of complete dimensional collapse, ties up an underlying continuum model for a pandemic with a simpler-seeming compartmental model, and will hopefully lead to new analysis of continuum models for epidemics.
    Keywords Quantitative Biology - Populations and Evolution ; Mathematics - Dynamical Systems
    Subject code 519
    Publishing date 2020-04-26
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

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  9. Book ; Online: New approximations, and policy implications, from a delayed dynamic model of a fast pandemic

    Vyasarayani, C. P. / Chatterjee, Anindya

    2020  

    Abstract: We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, ...

    Abstract We study an SEIQR (Susceptible-Exposed-Infectious-Quarantined-Recovered) model for an infectious disease, with time delays for latency and an asymptomatic phase. For fast pandemics where nobody has prior immunity and everyone has immunity after recovery, the SEIQR model decouples into two nonlinear delay differential equations (DDEs) with five parameters. One parameter is set to unity by scaling time. The subcase of perfect quarantining and zero self-recovery before quarantine, with two free parameters, is examined first. The method of multiple scales yields a hyperbolic tangent solution; and a long-wave approximation yields a first order ordinary differential equation (ODE). With imperfect quarantining and nonzero self-recovery, the long-wave approximation is a second order ODE. These three approximations each capture the full outbreak, from infinitesimal initiation to final saturation. Low-dimensional dynamics in the DDEs is demonstrated using a six state non-delayed reduced order model obtained by Galerkin projection. Numerical solutions from the reduced order model match the DDE over a range of parameter choices and initial conditions. Finally, stability analysis and numerics show how correctly executed time-varying social distancing, within the present model, can cut the number of affected people by almost half. Alternatively, faster detection followed by near-certain quarantining can potentially be even more effective.
    Keywords Quantitative Biology - Populations and Evolution ; Mathematics - Dynamical Systems
    Subject code 518
    Publishing date 2020-04-08
    Publishing country us
    Document type Book ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

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    Inter-library loan at ZB MED

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  10. Article ; Online: Author Correction

    Sankalp Tiwari / C. P. Vyasarayani / Anindya Chatterjee

    Scientific Reports, Vol 11, Iss 1, Pp 1-

    Data suggest COVID-19 affected numbers greatly exceeded detected numbers, in four European countries, as per a delayed SEIQR model

    2021  Volume 2

    Abstract: An amendment to this paper has been published and can be accessed via a link at the top of the paper. ...

    Abstract An amendment to this paper has been published and can be accessed via a link at the top of the paper.
    Keywords Medicine ; R ; Science ; Q
    Language English
    Publishing date 2021-05-01T00:00:00Z
    Publisher Nature Portfolio
    Document type Article ; Online
    Database BASE - Bielefeld Academic Search Engine (life sciences selection)

    Full text online

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