A mathematical model of epidemics with screening and variable infectivity

Kim, M. Y.; Milner, Fabio

doi:10.1016/0895-7177(95)00029-2

Cited by 18 publications

(18 citation statements)

References 16 publications

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“…Consequently, lim t i(t) = 0. Computation similar to (14) [but without δ] shows that ∞ 0 u(θ, t) dθ → 0, which implies that u(θ, t) → 0 for almost all θ. Assuming α(θ) is bounded, from the equation for the recovered class in (3) we see that lim t r(t) = 0.…”

Section: (T)mentioning

confidence: 99%

“…Under certain conditions, a stable endemic state may exist even when R 0 < 1, usually due to a phenomenon known as a "backward" bifurcation; in such cases, R 0 must be reduced well below 1 to ensure eradication of the disease. Variation in infectivity is also important to model when the disease's timescale is on the same order as the demographic timescale [14], as evidenced by the worldwide AIDS epidemic. Some diseases feature an initial infective period when symptoms and infectivity are high, followed by a low-level or chronic stage during which the body has already begun to mount an immune response to the infection, and symptoms and infectivity are sharply reduced.…”

Section: Introductionmentioning

confidence: 99%

“…Among others, Brauer [1], Kim & Milner [14] and Thieme & Castillo-Chavez [18] have studied the effects of variable infectivity on the spread of infectious diseases. The variable infectivity of HIV/AIDS in particular has had a tremendous impact on the shape of the AIDS epidemic which continues to skyrocket in many countries worldwide, and has rebounded following earlier attempts to contain it.…”

Section: Introductionmentioning

confidence: 99%

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Vaccination strategies and backward bifurcation in an age-since-infection structured model

Kribs-Zaleta

Martcheva

2002

Mathematical Biosciences

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We consider models for a disease with acute and chronic infective stages, and variable infectivity and recovery rates, within the context of a vaccination campaign. Models for SIRS and SIS disease cycles exhibit backward bifurcations under certain conditions, which complicate the criteria for success of the vaccination campaign by making it possible to have stable endemic states when R 0 < 1. We also show the extent to which the forms of the infectivity and recovery functions affect the possibility of backward bifurcations. SIR and SI models examined do not exhibit this behavior.

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Section: (T)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Vaccination strategies and backward bifurcation in an age-since-infection structured model

Kribs-Zaleta

Martcheva

2002

Mathematical Biosciences

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“…Thieme and C. Castillo-Chavez explored the role of variable infectivity together with a variable incubation period in the dynamics of HIV transmission in a homogeneously mixing population, and discussed both the asymptotical behavior of the equilibria and the possibility whether the undamped oscillations occur or not. In [2], M.Y. Kim and F.A.…”

Section: Introductionmentioning

confidence: 98%

“…However, the infection-age-dependent epidemic models were largely neglected until 1970s [16,17]. Recently, the infection-age-dependent epidemic models have been extensively considered (see, for examples, [2][3][4][5][6][7]). …”

Section: Introductionmentioning

confidence: 99%

A SIRS epidemic model with infection-age dependence

Zhang

Peng

2007

Journal of Mathematical Analysis and Applications

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Based on J. Mena-Lorca and H.W. Hethcote's epidemic model, a SIRS epidemic model with infectionage-dependent infectivity and general nonlinear contact rate is formulated. Under general conditions, the unique existence of its global positive solutions is obtained. Moreover, under more general assumptions than the existing, the existence and asymptotical stability of its equilibria are discussed. In the end, the condition on the stability of endemic equilibrium is verified by a special model.

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Incorporating infectious duration‐dependent transmission into Bayesian epidemic models

2022

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Compartmental models are commonly used to describe the spread of infectious diseases by estimating the probabilities of transitions between important disease states. A significant challenge in fitting Bayesian compartmental models lies in the need to estimate the duration of the infectious period, based on limited data providing only symptom onset date or another proxy for the start of infectiousness. Commonly, the exponential distribution is used to describe the infectious duration, an overly simplistic approach, which is not biologically plausible. More flexible distributions can be used, but parameter identifiability and computational cost can worsen for moderately sized or large epidemics. In this article, we present a novel approach, which considers a curve of transmissibility over a fixed infectious duration. The incorporation of infectious duration‐dependent (IDD) transmissibility, which decays to zero during the infectious period, is biologically reasonable for many viral infections and fixing the length of the infectious period eases computational complexity in model fitting. Through simulation, we evaluate different functional forms of IDD transmissibility curves and show that the proposed approach offers improved estimation of the time‐varying reproductive number. We illustrate the benefit of our approach through a new analysis of the 1995 outbreak of Ebola Virus Disease in the Democratic Republic of the Congo.

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A mathematical model of epidemics with screening and variable infectivity

Cited by 18 publications

References 16 publications

Vaccination strategies and backward bifurcation in an age-since-infection structured model

Vaccination strategies and backward bifurcation in an age-since-infection structured model

A SIRS epidemic model with infection-age dependence

Incorporating infectious duration‐dependent transmission into Bayesian epidemic models

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