A mathematical model of bilingualism

El-Owaidy, H. M.; Ismail, M. N.

doi:10.1016/s0096-3003(01)00157-6

Cited by 8 publications

(5 citation statements)

References 3 publications

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“…Baggs and Freedman modelled a mixed population with one bilingual and two monolingual components where one of the languages is dominant [11]. Furthermore, El-Owaidy and Ismail examined a more general model with one bilingual and three monolingual components [12]. In both research, they investigated equilibria system and its stability yielding criteria for the persistence or extinction of the dominated language speakers.…”

Section: Salma Al-tuwairqi and Lamees Felimbanmentioning

confidence: 99%

“…In this paper, we model the impact of English medium international schools on local language as a mathematical compartment model rather than predator-prey models presented in [11] and [12]. The aim of this work is to analyze the model by using stability theory of nonlinear differential equations to find an analytical threshold that helps maintain local languages and prevent language shift.…”

Section: Salma Al-tuwairqi and Lamees Felimbanmentioning

confidence: 99%

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The impact of international school on local language: a mathematical model

Al-Tuwairqi¹,

Felimban²

2014

ams

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This paper aims to analyze the impact of English medium international schools on local language. A mathematical compartment model is proposed. Two equilibrium points of the model are examined: English free equilibrium and English existence equilibrium. The basic reproduction number is found and the local stability of the equilibrium points is explored. Furthermore, an analytical threshold that helps maintain local languages and prevent language shift is established. Finally, we support our results using numerical simulations.

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Section: Salma Al-tuwairqi and Lamees Felimbanmentioning

confidence: 99%

Section: Salma Al-tuwairqi and Lamees Felimbanmentioning

confidence: 99%

The impact of international school on local language: a mathematical model

Al-Tuwairqi¹,

Felimban²

2014

ams

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“…They found that, besides the extinction of the monolingual group speaking the low-status language and of the bilingual group, coexistence between all three population groups and coexistence between the monolingual group speaking the high-status language and the bilingual group were possible. El-Owaidy and Ismail (2002) generalized this model by incorporating a third monolingual population group.…”

Section: Recent Modeling Approachesmentioning

confidence: 99%

Demography and Language Competition

Kandler

2009

Human Biology

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Attempts to describe language competition and extinction in a mathematical way have enjoyed increased popularity recently. In this paper I review recent modeling approaches and, based on these findings, propose a model of reaction-diffusion type. I analyze the dynamics of interactions of a population with two monolingual groups and a group that is bilingual in these two languages. The results show that demographic factors, such as population growth or population dispersal, play an important role in the competition dynamic. Furthermore, I consider the impact of two strategies for language maintenance: adjusting the status of the endangered language and adjusting the availability of monolingual and bilingual educational resources. Keywordslanguage competition, language extinction, language maintenance, population growth, population dispersal, reaction dispersal competition model, agent-based models. Cover Page FootnoteI thank Stephan Shennan and James Steele, the organizers of the Arts and Humanities Research Council (AHRC) Centre for the Evolution of Cultural Diversity (CECD) workshop "Demographic Processes and Cultural Change," for the opportunity to present this work to an expert audience. I am also grateful to James Steele for helpful discussions and to two anonymous reviewers for constructive comments on the manuscript. Funding was provided by a Leverhulme Trust Early Career Fellowship.This open access article is available in Human Biology: http://digitalcommons.wayne.edu/humbiol/vol81/iss2/5 Demography and Language CompetitionAnne Kandler 1 Abstract Attempts to describe language competition and extinction in a mathematical way have enjoyed increased popularity recently. In this paper I review recent modeling approaches and, based on these fi ndings, propose a model of reaction-diffusion type. I analyze the dynamics of interactions of a population with two monolingual groups and a group that is bilingual in these two languages. The results show that demographic factors, such as population growth or population dispersal, play an important role in the competition dynamic. Furthermore, I consider the impact of two strategies for language maintenance: adjusting the status of the endangered language and adjusting the availability of monolingual and bilingual educational resources.Language competition and death is a phenomenon that can be observed worldwide. Linguists estimate that there are 5,000-6,700 languages in the world today, but because of an explosive spread of a few dominant languages (e.g., English or Chinese), at least half of them will become extinct in the 21st century (Krauss 1992). The processes that lead to the disappearance of languages have greatly accelerated over the past 200 years, and this worrying rate of extinction is probably unique to our time (Grenoble and Whaley 2006). A number of different socioeconomic, political, and cultural factors can be identifi ed as driving this decline of linguistic diversity. In the course of globalization and of recent trends for urbanization and lon...

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“…Any similarities must therefore be at a very deep level and require considerable abstraction. Subsequent papers by the same authors Freedman (1991, 1993)) and by El-Owaidy and Ismail (2002) further develop the model while retaining this abstract approach.…”

Section: Bilingualismmentioning

confidence: 99%

The Future of Bilingualism: An Application of the Baggs and Freedman Model

Wyburn

Hayward

2008

The Journal of Mathematical Sociology

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The original paper (Baggs and Freedman, 1990) gave a model of the interaction of a bilingual with a unilingual population. This paper examines the original in an exhaustive fashion and identifies four possible scenarios in the long-term future of the bilingual population. Equilibrium points are found in a manner conducive to practical interpretation, and their stability is investigated. The original model is then applied to the situation in modern Wales and more briefly to that in Scotland, Ireland and Brittany. In conclusion the capacity of the model to inform policy is considered, and an amended model is suggested.

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A mathematical model of bilingualism

Cited by 8 publications

References 3 publications

The impact of international school on local language: a mathematical model

The impact of international school on local language: a mathematical model

Demography and Language Competition

The Future of Bilingualism: An Application of the Baggs and Freedman Model

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