Modeling the effects of carriers on transmission dynamics of infectious diseases

Kalajdzievska, Darja; Li, Michael Yi

doi:10.3934/mbe.2011.8.711

Cited by 35 publications

(18 citation statements)

References 12 publications

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“…This more realistic distinction have contrasted with some models (e.g. [16]) where these two classes are combined and constitutes an improvement. We investigated the effects of the efficacy of the vaccine and asymptomatic carriers (or "lost of sight") on the spread of infectious diseases.…”

Section: Calculation Of Bmentioning

confidence: 99%

“…Others studies using large-scale computational models with carriers are aimed at other diseases [9,22,23]. More recently, a model in [16] was proposed to analyze the effects of carriers on the transmission dynamics of diseases. In their work [16], the authors considered an efficacy vaccine, i.e the recovered and vaccinated subgroups are not distinguished, and did not take into account of the effect of ineffectiveness of vaccination.…”

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confidence: 99%

“…Therefore, the objective of this work is threefold: (1) -to propose a more general mathematical model extending the works in [14][15][16] by the incorporation of the effectiveness of vaccination and multiple doses/stages of vaccines; (2) -to rigorously analyze the resulting model by addressing the global stability of the model; (3)to perform local and global sensitivity analyses of the basic reproduction and the numerical simulations through which, the impacts of the effectiveness of both the vaccination and the presence asymptomatic carriers on the transmission of some infectious diseases (e.g. HBV infection).…”

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confidence: 99%

“…The model is constructed based on the model proposed in [16]. We make a more realistic assumption that the vaccine is not totally effective, and extend this model by incorporating three vaccinated classes,…”

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confidence: 99%

“…We have also carried out numerical simulations to illustrate our theoretical results. The Lyapunov functions used in this paper to prove the global stability of endemic equilibrium have the same form as those used in [14][15][16]18].…”

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confidence: 99%

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Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Manyombe

Mbang²,

Lubuma³

et al. 2016

MBE

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In this paper, an epidemic model is investigated for infectious diseases that can be transmitted through both the infectious individuals and the asymptomatic carriers (i.e., infected individuals who are contagious but do not show any disease symptoms). We propose a dose-structured vaccination model with multiple transmission pathways. Based on the range of the explicitly computed basic reproduction number, we prove the global stability of the disease-free when this threshold number is less or equal to the unity. Moreover, whenever it is greater than one, the existence of the unique endemic equilibrium is shown and its global stability is established for the case where the changes of displaying the disease symptoms are independent of the vulnerable classes. Further, the model is shown to exhibit a transcritical bifurcation with the unit basic reproduction number being the bifurcation parameter. The impacts of the asymptomatic carriers and the effectiveness of vaccination on the disease transmission are discussed through through the local and the global sensitivity analyses of the basic reproduction number. Finally, a case study of hepatitis B virus disease (HBV) is considered, with the numerical simulations presented to support the analytical results. They further suggest that, in high HBV prevalence countries, the combination of effective vaccination (i.e. ≥ 3 doses of HepB vaccine), the diagnosis of asymptomatic carriers and the treatment of symptomatic carriers may have a much greater positive impact on the disease control.

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Section: Calculation Of Bmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Manyombe

Mbang²,

Lubuma³

et al. 2016

MBE

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Modeling biological control of carrier‐dependent infectious diseases

Misra

Gupta

Venturino

2020

Comp and Math Methods

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Since decades, hazardous chemicals are used to control the growth of carriers (flies, ticks, mites, and so on) in the environment, which are responsible for the spread of many infectious diseases, such as typhoid fever, polio, and some skin infections such as leprosy, and so on. Although these chemicals reduce the carrier population, they also inflict a sizeable harm to nontarget populations, like the human population. In this study, we present a mathematical model to control the carrier population using biological agents, which leads to the control of carrier-dependent infectious diseases. It is assumed that the disease can spread in the human population due to the direct contact between susceptible and infected individuals, but also indirectly through the vector population. The feasibility and stability of the system's equilibria are discussed. The key parameters of the proposed model are identified and their role in the transmission and control of such diseases is discussed. Our findings show that combined actions of two strategies, the biological control of carriers via parasitic wasps that target the immature stage of the flies and any extra exogenous means which eradicate the adult carriers when their population is at low levels, could be an effective and low cost approach to lessen the disease propagation.

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A periodic disease transmission model with asymptomatic carriage and latency periods

Al-Darabsah

Yuan

2017

J. Math. Biol.

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In this paper, the global dynamics of a periodic disease transmission model with two delays in incubation and asymptomatic carriage periods is investigated. We first derive the model system with a general nonlinear incidence rate function by stage-structure. Then, we identify the basic reproduction ratio [Formula: see text] for the model and present numerical algorithm to calculate it. We obtain the global attractivity of the disease-free state when [Formula: see text] and discuss the disease persistence when [Formula: see text]. We also explore the coexistence of endemic state in the nonautonomous system and prove the uniqueness with constants coefficients. Numerical simulations are provided to present a case study regarding the meningococcal meningitis disease transmission and discuss the influence of carriers on [Formula: see text].

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Modeling the effects of carriers on transmission dynamics of infectious diseases

Cited by 35 publications

References 12 publications

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Global dynamics of a vaccination model for infectious diseases with asymptomatic carriers

Modeling biological control of carrier‐dependent infectious diseases

A periodic disease transmission model with asymptomatic carriage and latency periods

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