A New Mathematical Model of Syphilis

Milner, Fabio; Zhao, Ruijun

doi:10.1051/mmnp/20105605

Cited by 32 publications

(21 citation statements)

References 22 publications

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“…[83]—syphilis and gonorrhoeacondom use—Morin et al . [84]— Gray et al [85]—vaccination—Milner & Zhao [86]———reduce sexual risk—Milner & Zhao [86]———social distancing—Aadland et al . [87]— Gray et al [85] Althouse & Hébert-Dufresne [88]measles and pertussisvaccinationBhattacharyya & Bauch [89], Shim et al .…”

Section: Resultsmentioning

confidence: 99%

“…The largest category embodies 76 references managing information as a dynamic parameter [3,25,34,40,43,47–50,53,55,60,61,65–68,70,71,74,77,80,82,86,92,94–96,99,100,102,104–109,113,115–117,119–126,128–131,133,134,137,148,149,153,157,161,165,166,168,171–178,184–186,188,189]. In this category, instead of a threshold, the information is a continuous input in the decision-making process of individuals.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Behavioural change models for infectious disease transmission: a systematic review (2010–2015)

Verelst

Willem

Beutels

2016

J. R. Soc. Interface.

325

323

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We review behavioural change models (BCMs) for infectious disease transmission in humans. Following the Cochrane collaboration guidelines and the PRISMA statement, our systematic search and selection yielded 178 papers covering the period 2010–2015. We observe an increasing trend in published BCMs, frequently coupled to (re)emergence events, and propose a categorization by distinguishing how information translates into preventive actions. Behaviour is usually captured by introducing information as a dynamic parameter (76/178) or by introducing an economic objective function, either with (26/178) or without (37/178) imitation. Approaches using information thresholds (29/178) and exogenous behaviour formation (16/178) are also popular. We further classify according to disease, prevention measure, transmission model (with 81/178 population, 6/178 metapopulation and 91/178 individual-level models) and the way prevention impacts transmission. We highlight the minority (15%) of studies that use any real-life data for parametrization or validation and note that BCMs increasingly use social media data and generally incorporate multiple sources of information (16/178), multiple types of information (17/178) or both (9/178). We conclude that individual-level models are increasingly used and useful to model behaviour changes. Despite recent advancements, we remain concerned that most models are purely theoretical and lack representative data and a validation process.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Behavioural change models for infectious disease transmission: a systematic review (2010–2015)

Verelst

Willem

Beutels

2016

J. R. Soc. Interface.

325

323

View full text Add to dashboard Cite

show abstract

“…However, this equilibrium may not be globally asymptotically stable in Ω for

R < 1

, owing to the possibility of backward bifurcation. A backward bifurcation is possible when the stable DFE co-exists with a stable endemic equilibrium for

R < 1

(Agusto and Gumel, 2010; Dushoff et al, 1998; Milner and Zhao, 2010; Garba et al, 2008). The public health implication of backward bifurcation is that the classical requirement of having the reproduction number less than unity, although necessary, is no longer sufficient for disease control.…”

Section: Model Analysismentioning

confidence: 99%

The impact of bed-net use on malaria prevalence

Agusto

Valle

Blayneh

et al. 2013

Journal of Theoretical Biology

107

132

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Malaria infection continues to be a major problem in many parts of the world including the Americas, Asia, and Africa. Insecticide-treated bed-nets have shown to reduce malaria cases by 50%; however, improper handling and human behavior can diminish their effectiveness. We formulate and analyze a mathematical model that considers the transmission dynamics of malaria infection in mosquito and human populations and investigate the impact of bed-nets on its control. The effective reproduction number is derived and existence of backward bifurcation is presented. The backward bifurcation implies that the reduction of scriptR below unity alone is not enough to eradicate malaria, except when the initial cases of infection in both populations are small. Our analysis demonstrate that bed-net usage has a positive impact in reducing the reproduction number scriptR. The results show that if 75% of the population were to use bed-nets, malaria could be eliminated. We conclude that more data on the impact of human and mosquito behavior on malaria spread is needed to develop more realistic models and better predictions.

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“…The susceptible-infective-susceptible (SIS) model is employed in studying infections such as Gonorrhea [31] as there is a possibility of host becoming susceptible to infection once again. The susceptible-infective-recovered (SIR) model is employed to understand diseases such as Syphilis [33], wherein, immunity lasts for a limited period before waning such that the individual is once again susceptible. Dynamics of such systems are generally studied from two perspectives, (i) stability of disease-free equilibrium, and (ii) stability of endemic equilibrium.…”

Section: Introductionmentioning

confidence: 99%

A dynamic model for infectious diseases: The role of vaccination and treatment

Rao¹,

Kumar

2015

Chaos, Solitons & Fractals

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This article is dedicated to their research supervisor Prof. V. Sree Hari Rao for his continued inspiration. a b s t r a c tUnderstanding dynamics of an infectious disease helps in designing appropriate strategies for containing its spread in a population. Recent mathematical models are aimed at studying dynamics of some specific types of infectious diseases. In this paper we propose a new model for infectious diseases spread having susceptible, infected, and recovered populations and study its dynamics in presence of incubation delays and relapse of the disease. The influence of treatment and vaccination efforts on the spread of infection in presence of time delays are studied. Sufficient conditions for local stability of the equilibria and change of stability are derived in various cases. The problem of global stability is studied for an important special case of the model. Simulations carried out in this study brought out the importance of treatment rate in controlling the disease spread. It is observed that incubation delays have influence on the system even under enhanced vaccination. The present study has clearly brought out the fact that treatment rate even in presence of time delays would contain the disease as compared to popular belief that eradication can only be done through vaccination.

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A New Mathematical Model of Syphilis

Cited by 32 publications

References 22 publications

Behavioural change models for infectious disease transmission: a systematic review (2010–2015)

Behavioural change models for infectious disease transmission: a systematic review (2010–2015)

The impact of bed-net use on malaria prevalence

A dynamic model for infectious diseases: The role of vaccination and treatment

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