Mathematical Biosciences and Engineering (MBE)

Sociological phenomena as multiple nonlinearities: MTBI's new metaphor for complex human interactions
Pages: 1587 - 1607, Issue 5/6, October/December 2013

doi:10.3934/mbe.2013.10.1587      Abstract        References        Full text (273.3K)                  Related Articles

Christopher M. Kribs-Zaleta - Mathematics Department, University of Texas at Arlington, Box 19408, Arlington, TX 76019-0408, United States (email)

1 Carlos A. Acevedo-Estefania, Christina Gonzalez, Karen R. Rios-Soto, Eric D. Summerville, Baojun Song and Carlos Castillo-Chavez, A mathematical model for lung cancer: The effects of second-hand smoke and education, Biometrics Unit Technical Report BU-1525-M, Cornell University, 2000. Available from: http://mtbi.asu.edu/research/archive.
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4 Luís M. A. Bettencourt, Ariel Cintrón-Arias, David I. Kaiser and Carlos Castillo-Chavez, The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models, Physica A, 364 (2006), 513-536.
5 Corvina D. H. Boyd, Alison Castro, Nicolás Crisosto, Arlene Morales Evangelista, Carlos Castillo-Chavez and Christopher Kribs-Zaleta, A socially transmitted disease: Teacher qualifications and dropout rates, Studies in Theoretical Biology: A Collection of Undergraduate Research, 1 (2000), 549-580; Biometrics Unit Technical Report BU-815, Cornell University. Available from: http://mtbi.asu.edu/research/archive.
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7 Carlos Castillo-Garsow, Guarionex Jordán-Salivia and Ariel Rodriguez-Herrera, Mathematical models for the dynamics of tobacco use, recovery, and relapse, Biometrics Unit Technical Report BU-1505-M, Cornell University, 1997. Available from: http://mtbi.asu.edu/research/archive.
8 Jonathan Crane, The epidemic theory of ghettos and neighborhood effects on dropping out and teenage childbearing, Amer. J. Soc., 95 (1989), 1226-1259.
9 Nicolás Crisosto, Christopher Kribs-Zaleta, Carlos Castillo-Chavez and Stephen Wirkus, Community resilience in collaborative learning, Discrete and Continuous Dynamical Systems, Series B, 14 (2010), 17-40.       
10 O. Diekmann, J. A. P. Heesterbeek and J. A. J. Metz, On the definition and the computation of the basic reproduction ratio $R_0$ in models for infectious diseases in heterogeneous population, Journal of Mathematical Biology, 28 (1990), 365-382.       
11 Jennifer L. Dillon, Natalia Baeza, Mary Cristina Ruales and Baojun Song, A mathematical model of depression in young women as a function of the pressure to be "beautiful,'' Biometrics Unit Technical Report BU-1616-M, Cornell University, 2002. Available from: http://mtbi.asu.edu/research/archive.
12 Arlene Morales Evangelista, Angela R. Ortiz, Karen R. Ríos-Soto and Alicia Urdapilleta, USA the fast food nation: Obesity as an epidemic, MCMSC Technical Report MTBI-01-3M, Arizona State University, 2004. Available from: http://mtbi.asu.edu/research/archive.
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15 Beverly González, Emilia Huerta-Sánchez, Angela Ortiz-Nieves, Terannie Vázquez-Álvarez and Christopher Kribs-Zaleta, Am I too fat? Bulimia as an epidemic, Journal of Mathematical Psychology, 47 (2003), 515-526.       
16 Mark Granovetter, Threshold models of collective behavior, Am. J. Soc., 83 (1978), 1420-1443.
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19 Karl P. Hadeler and Carlos Castillo-Chávez, A core group model for disease transmission, Math. Biosciences, 128 (1995), 41-55.
20 J. A. P. Heesterbeek, A brief history of $R_0$ and a recipe for its calculation, Acta Biotheoretica, 50 (2002), 189-204.
21 W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. Part I, Proc. Royal Soc. Edin. A, 115 (1927), 700-721; Reprinted in Bull. Math. Biol., 53 (1991), 33-55.
22 W. O. Kermack and A. G. McKendrick, Contributions to the mathematical theory of epidemics. II. The problem of endemicity, Proc. Royal Soc. Edin. A, 138 (1932), 55-83; Reprinted in Bull. Math. Biol., 53 (1991), 57-87.
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24 Christopher M. Kribs-Zaleta, Alternative transmission modes for Trypanosoma cruzi, Math. Biosci. Eng., 7 (2010), 657-673.       
25 Christopher M. Kribs-Zaleta and Jorge X. Velasco-Hernández, A simple vaccination model with multiple endemic states, Math. Biosciences, 164 (2000), 183-201.
26 Anuj Mubayi, Priscilla E. Greenwood, Carlos Castillo-Chavez, Paul Gruenewald and Dennis M. Gorman, Impact of relative residence times on the distribution of heavy drinkers in highly distinct environments, Socio-Economic Planning Sciences, 43 (2010), 1-12.
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29 Tönu Puu, "Nonlinear Economic Dynamics,'' Springer-Verlag, New York, 1992.
30 Daniel M. Romero, Christopher M. Kribs-Zaleta, Anuj Mubayi and Clara Orbe, An epidemiological approach to the spread of political third parties, Discrete and Continuous Dynamical Systems, Series B, 15 (2011), 707-738.       
31 Ronald Ross, "The Prevention of Malaria,'' Second edition, Murray, London, 1911.
32 Fabio Sánchez, Xiaohong Wang, Carlos Castillo-Chavez, Dennis M. Gorman and Paul J. Gruenewald, Drinking as an epidemic: A simple mathematical model with recovery and relapse, in "Therapist's Guide to Evidence-Based Relapse Prevention'' (eds. Katie Witkiewitz and G. Alan Marlatt), Academic Press/Elsevier, (2007), 353-368.
33 Thomas Schelling, Dynamic models of segregation, J. Math. Soc., 1 (1971), 143-186.
34 Susan Seal, William Z. Rayfield, Carl Ballard II, Holden Tran, Christopher Kribs-Zaleta and Edgar Díaz, A dynamical interpretation of the three-strikes law, MCMSC Technical Report MTBI-04-07M, Arizona State University, 2007. Available from: http://mtbi.asu.edu/research/archive.
35 Baojun Song, Melissa Castillo-Garsow, Karen R. Ríos-Soto, Marcin Mejran, Leilani Henson and Carlos Castillo-Chavez, Raves, clubs, and ecstasy: The impact of peer pressure, Mathematical Biosciences and Engineering, 3 (2006), 249-266.       
36 Pauline Van den Driessche and James Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical Biosciences, 180 (2002), 29-48.       
37 Wolfgang Weidlich, Synergetic modelling concepts for sociodynamics with application to collective political opinion formation, J. Math. Soc., 18 (1994), 267-291.
38 Wolfgang Weidlich, "Sociodynamics. A Systematic Approach to Mathematical Modelling in the Social Sciences,'' Harwood Academic Publishers, Amsterdam, 2000.       

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