Mathematical Study of the Impact of Quarantine, Isolation and Vaccination in Curtailing an Epidemic

Podder, Chandra Nath; Gumel, Abba B.; Bowman, Chris; McLeod, Robert G.

doi:10.1142/s0218339007002180

Cited by 12 publications

(12 citation statements)

References 16 publications

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“…The various types of classical epidemic models with quarantine/isolation have been investigated in many articles. See, for example [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

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The global dynamics for a stochastic SIS epidemic model with isolation

Chen

Wen

Teng

2018

Physica A: Statistical Mechanics and its Applications

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Section: Introductionmentioning

confidence: 99%

“…Motivated by the works [1,2,4,5,[29][30][31][32], in this paper as an extension of model (1.1) we firstly assume that the diseaserelated death rates of isolation and no-isolation are different, respectively, denote by α 2 and α 3 . Then, we further define µ 1 = µ, µ 2 = µ+α 2 and µ 3 = µ+α 3 for the convenience.…”

Section: Introductionmentioning

confidence: 99%

The global dynamics for a stochastic SIS epidemic model with isolation

Chen

Wen

Teng

2018

Physica A: Statistical Mechanics and its Applications

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“…It is worth stating, however, that the simulation results presented in this study are sensitive to the choices of parameter and initial values used in the simulations. The uncertainties associated with the parameters related to the testing and treatment rates are accounted for by considering three (arbitrarily chosen) effectiveness levels of the combined testing and treatment strategy (a more detailed uncertainty analysis, based on Latin hypercube sampling [4,5,27,32] for example, can be applied if more data (related to the testing and treatment rates) becomes available). …”

Section: Discussionmentioning

confidence: 99%

Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV

Podder

Sharomi

Gumel

et al. 2011

Differ Equ Dyn Syst

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This paper presents a deterministic model for evaluating the impact of anti-retroviral drugs (ARVs), voluntary testing (using standard antibody-based and a DNAbased testing methods) and condom use on the transmission dynamics of HIV in a community. Rigorous qualitative analysis of the model show that it has a globally-stable disease-free equilibrium whenever a certain epidemiological threshold, known as the effective reproduction number (R eff ), is less than unity. The model has an endemic equilibrium whenever R eff > 1. The endemic equilibrium is shown to be locally-asymptotically stable for a special case. Numerical simulations of the model show that the use of the combined testing and treatment strategy is more effective than the use of the standard ELISA testing method with ARV treatment, even for the use of condoms as a singular strategy. Furthermore, the universal strategy (which involves the use of condoms, the two testing methods and ARV treatment) is always more effective than the combined use of the standard ELISA testing method and ARVs.

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“…., m. It follows, from (ii), that a i E i $ Proof. Consider the reduced model, given by (20) with (21). Let R cr > 1, so that the associated unique endemic equilibrium exists.…”

Section: Acknowledgmentsmentioning

confidence: 99%

“…Substituting the expressions of the derivatives from the system (20), using (21), gives (note that the relation…”

Section: Acknowledgmentsmentioning

confidence: 99%

Qualitative study of a quarantine/isolation model with multiple disease stages

Safi

Gumel

2011

Applied Mathematics and Computation

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j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / a m c Newcastle disease and rabies [11,14]. It is known, however, that quarantine and isolation measures, especially in the context of a new emerging disease, are initially not administered effectively, but are gradually refined (as more data and knowledge of the disease transmission process becomes available (see, for instance, [8])).Numerous mathematical modeling work have been carried out to assess the impact of quarantine and isolation in combatting the spread of the diseases (such as some of the aforementioned modeling studies for SARS). However, many of the models used for assessing the impact of the quarantine and isolation measures tend to be built based on the assumption that the disease stages are exponentially distributed. However, some recent studies [7,30] show that it is more realistic to use gamma distribution assumption for the waiting time in the disease stages (rather than exponential distribution assumption). Furthermore, Feng et al. [7] showed that quarantine and isolation models that assume exponential distribution (for the disease stages) may not be suitable for diseases with relatively long latent and/or infectious periods for the case when isolation is not completely effective (i.e., isolated individuals can transmit infection).The purpose of the current study is to provide a rigorous qualitative analysis of a new deterministic model for transmission dynamics of a communicable disease, subject to the use of quarantine and isolation, where the waiting time in the associated infected classes are assumed to have gamma distribution. The model to be designed extends the SEIQHR model given in [24] by considering multiple stages of the exposed, infectious, quarantined and hospitalized individuals (unlike in [24], it is assumed here that hospitalized individuals do not transmit the infection). Diseases like HIV [25] and influenza [6] are known to have multiple disease (infection) stages.The paper is organized as follows. The model is formulated in Section 2. The global asymptotic stability of the disease-free equilibrium (DFE) is established in Section 3. The existence of the endemic equilibrium is analyzed in Section 4. Local and global stability proofs for the endemic equilibrium, for special cases, are also provided using a Krasnoselskii sub-linearity trick and a non-linear Lyapunov function of Goh-Voltera type, respectively.

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Mathematical Study of the Impact of Quarantine, Isolation and Vaccination in Curtailing an Epidemic

Cited by 12 publications

References 16 publications

The global dynamics for a stochastic SIS epidemic model with isolation

The global dynamics for a stochastic SIS epidemic model with isolation

Mathematical Analysis of a Model for Assessing the Impact of Antiretroviral Therapy, Voluntary Testing and Condom Use in Curtailing the Spread of HIV

Qualitative study of a quarantine/isolation model with multiple disease stages

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