Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay

Eckalbar, John C.; Eckalbar, Walter L.

doi:10.1016/j.biosystems.2014.12.004

“…Instead, it assumes a well-mixed population for which the crucial dynamics of disease transmission between individuals are lumped into the basic reproduction number R 0 , a macroscopic parameter describing the mean number of secondary transmissions from each infection. In practice, this quantity is used as a fitting parameter-limiting projection capabilities when the interactions between individuals change even slightly [7][8][9][10][11][12]. A recent example highlighting this deficiency is the spread of COVID-19 in China: containment policies imposing spatial barriers and suppressing individual interactions are thought to have hindered exponential growth of infection, yet this pivotal effect cannot be captured by the classic SIR model without invoking additional fitting parameters [13].…”

Section: Introductionmentioning

confidence: 99%

Infection Percolation: A Dynamic Network Model of Disease Spreading

Browne

¹

,

Amchin

²

,

Schneider

³

et al. 2021

Front. Phys.

4

0

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Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads through a social network as a traveling wave of infection, followed by a traveling wave of recovery, with the onset and dynamics of spreading determined by the interplay between disease transmission and recovery. We use these insights to develop a scaling theory that predicts the dynamics of infection for diverse diseases and populations. Furthermore, we show how spatial heterogeneities in susceptibility to infection can either exacerbate or quell the spread of disease, depending on its infectivity. Ultimately, our dynamic network approach provides a simple way to model disease spreading that unifies previous findings and can be generalized to diverse diseases, containment strategies, seasonal conditions, and community structures.

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“…Instead, it assumes a well-mixed population for which the crucial dynamics of disease transmission between individu-als are lumped into the basic reproduction number R 0 , a macroscopic parameter describing the mean number of secondary transmissions from each infection. In practice, this quantity is used as a fitting parameter-limiting projection capabilities when the interactions between individuals change even slightly [7][8][9][10][11][12]. A recent example highlighting this deficiency is the spread of COVID-19 in China: containment policies imposing spatial barriers and suppressing individual interactions are thought to have hindered exponential growth of infection, yet this pivotal effect cannot be captured by the classic SIR model without invoking additional fitting parameters [13].…”

Section: Introductionmentioning

confidence: 99%

Infection percolation: A dynamic network model of disease spreading

Browne,

Amchin,

Schneider

et al. 2021

Preprint

0

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Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads through a social network as a traveling wave of infection, followed by a traveling wave of recovery, with the onset and dynamics of spreading determined by the interplay between disease transmission and recovery. We use these insights to develop a scaling theory that predicts the dynamics of infection for diverse diseases and populations. Furthermore, we show how spatial heterogeneities in susceptibility to infection can either exacerbate or quell the spread of disease, depending on its infectivity. Ultimately, our dynamic network approach provides a simple way to model disease spreading that unifies previous findings and can be generalized to diverse diseases, containment strategies, seasonal conditions, and community structures.

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“…It has been used to tackle diseases such as measles, mumps, rubella, diphtheria, tetanus, influenza, polio, etc. Recently, the epidemiological models with vaccination strategy have been analyzed by many authors in [19][20][21][22][23][24][25][26][27]. For example, Li et al [19] discussed the global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria; Liu et al [20] established two SVIR models by considering the time for them to obtain immunity and the possibility for them to be infected before this; Trawicki [21] proposes a new SEIRS model with vital dynamics (birth and death rates), vaccination, and temporary immunity provides a mathematical description of infectious diseases and corresponding spread in biology; T.K.…”

Section: Introductionmentioning

confidence: 99%

“…Kar et al [23] focused on the study of a nonlinear mathematical SIR epidemic model with a vaccination program, and the results showed that an accurate estimation of the efficiency of vaccination is necessary to prevent and control the spread of disease. We also refer the readers to [26,27] for relative studies on this respect. Elimination is also an effective measure to eliminate the source of infection, it is that the infected individuals were killed when they are found.…”

Section: Introductionmentioning

confidence: 99%

Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

Ma

¹

,

Liu

²

,

Li

³

2018

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In this paper, an SIQR (Susceptible, Infected, Quarantined, Recovered) epidemic model with vaccination, elimination, and quarantine hybrid strategies is proposed, and the dynamics of this model are analyzed by both theoretical and numerical means. Firstly, the basic reproduction number R 0 , which determines whether the disease is extinct or not, is derived. Secondly, by LaSalles invariance principle, it is proved that the disease-free equilibrium is globally asymptotically stable when R 0 < 1 , and the disease dies out. By Routh-Hurwitz criterion theory, we also prove that the disease-free equilibrium is unstable and the unique endemic equilibrium is locally asymptotically stable when R 0 > 1 . Thirdly, by constructing a suitable Lyapunov function, we obtain that the unique endemic equilibrium is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists when R 0 > 1 . Finally, some numerical simulations are presented to illustrate the analysis results.

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Dynamics of an SIR model with vaccination dependent on past prevalence with high-order distributed delay

Cited by 12 publications

References 36 publications

Infection Percolation: A Dynamic Network Model of Disease Spreading

Infection Percolation: A Dynamic Network Model of Disease Spreading

Infection percolation: A dynamic network model of disease spreading

Global Dynamics of an SIQR Model with Vaccination and Elimination Hybrid Strategies

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