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Revista de Divulgación del INSTITUTO DE MEDICINA FORENSE de la UNIVERSIDAD VERACRUZANA

2020, Number 4

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Rev Mex Med Forense 2020; 5 (4)

Mexican mathematics and its fight against Dengue: Achievements and challenges

Ortigoza CGM, Lorandi MAP

Language: Spanish
References: 64
Page: 35-60
PDF size: 733.57 Kb.


ABSTRACT

In this work, we made a review of some of the mathematical models that have been used by mexican mathematicians to model and simulate the spread of Dengue. Either deterministic, empirical, or statistical analysis models are discussed. Posing in some cases control measures to reduce or prevent the spread of dengue. Both deterministic models or statistical analyzes are reviewed: methodologies that involve analysis, modeling and simulation, successful cases of their applications for the calculation of specific quantities and of importance for health experts are listed and classified as the basic reproduction number or the risk of contagion analysis. Reflections of the challenges and future implications that should be included in the mathematical models to simulate the prevention and control of the spread of dengue in Mexico are also included.Some of the extensions that have been made to the traditional models and the added variables are listed, successful cases of their applications for the calculation of specific important quantities for health experts such as: the basic reproduction number or the risk analysis of infection. Reflections of the challenges and future modifications that should be included in the models to simulate Dengue spread are included.


REFERENCES

  1. Torres-Briones HA. Impacto económico del dengue en México por regiones epidemiológicas (tesis de licenciatura): Universidad Autónoma de San Luis Potosí; 2018.

  2. Brauer F, Castillo-Chavez C, Mubayi A, Towers S. Some models for epidemics of vector-transmitted diseases. Infectious disease modelling. 2016; 1(1): p. 79 - 87.

  3. Reiner R, Perkins A, Barker C, Niu T, Chaves L, Ellis A, et al. A systematic review of mathematical models of mosquito-borne pathogen transmission. Journal of The Royal Society Interface. 2013; 10(81): p. 1970–2010.

  4. Chen D. Modeling the Spread of Infectious Diseases: A Review chapter 2. En Analyzing and modeling spatial and temporal dynamics of infectious diseases.: John Wiley & Sons; 2014. p. 19 - 42.

  5. Duan W, Fan Z, Zhang P, Guo G, Quio X. Mathematical and computational approaches to epidemic modeling: a comprehensive review. Frontiers of Computer Science. 2015; 9(5): p. 806 – 826.

  6. OPS. Caos reportados de dengue en las américas. [Online]; 2020. Disponible en: http://www.paho.org/data/index.php/es/temas/indicadores-dengue/dengue-nacional/9-dengue-pais-anohtml.

  7. Gómez-Dantés H, Montesano-Castellanos R, López-Moreno S, Tapia-Conyer R. El dengue en México: Situación epidemiológica reciente. Gaceta médica de México. 1995; 131(2): p. 237 - 240.

  8. CONAGUA. CONAGUA. [Online]; 2020. Disponible en: https://smn.conagua.gob.mx/es/climatologia/temperaturas-y-lluvias/resumenes-mensuales-de-temperaturas-y-lluvias.

  9. Koopman J, Prevots D, Vaca-Marin M, Gomez-Dantes H, Aquino MZ, Longini I, et al. Determinants and Predictors of Dengue Infection in Mexico. American Journal of Epidemiology. 1991; 133(11): p. 1168 - 1178.

  10. Farfán-Ale JA, Loroño-Pino MA. Incidencia de infección por virus dengue en niños de 8 a 14 años de edad radicados en las áreas urbana y rural del municipio de Mérida, Yucatán. Boletín Médico Hospital Infantil Mexicano. 1991; 48(11): p. 780 - 784.

  11. Prevots DR. The effect of human mobility on the geographic spread of dengue fever in Mexico (tesis doctoral): Michigan University; 1991.

  12. Herrera-Basto E, Prevots D, Zarate M, Silva J, Sepulveda-Amor J. First reported outbreak of classical dengue fever at 1,700 meters above sea level in Guerrero State, Mexico, June 1988. The American journal of tropical medicine and hygiene. 1992; 46(6): p. 649 - 653.

  13. Gómez-Dantés H, Montesano-Castellanos R, López-Moreno S, Tapia R. El dengue en México. Situación epidemiológica reciente. Gaceta médica de México. 1995; 131(2): p. 237 - 240.

  14. Montesano R, Ruiz C. Vigilancia Epidemiológica del dengue en México. Salud Pública de México. 1995; 37(su1): p. 64 - 76.

  15. Narro J, Gómez H. El dengue en México un problema prioritario de salud pública. Salud Pública de México. 1995; 37(su1): p. 12 - 20.

  16. Newton E, Reiter P. A model of the transmission of dengue fever with an evaluation of the impact of ultra-low volume (ULV) insecticide applications on dengue epidemics. The American journal of tropical medicine and hygiene. 1992; 47(6): p. 709 - 720.

  17. Feng Z, Velasco J. Competitive exclusion in a vector-host model for dengue fever. Journal of mathematical biology. 1997; 35(5): p. 523 - 544.

  18. Esteva L, Vargas C. Analysis of a dengue disease transmission model. Mathematical Biosciences. 1998; 150(2): p. 131 - 151.

  19. Esteva L, Vargas C. A model for dengue disease with variable human population. Journal of mathematical biology. 1999; 38(3): p. 220 - 240.

  20. Ritchie J, Méndez J. Evaluating epidemic interventions policies with system thinking: A case study of dengue fever in Mexico. The Journal of the System Dynamics Society. 1999; 15(2): p. 119 - 138.

  21. Escoba J, Gómez H. Determinantes de la transmisión de dengue en Veracruz: un abordaje ecológico para su control. Salud pública de México. 2003; 45(1): p. 43 - 53.

  22. Espinoza F, Hernández C, Rendón R, Carrillo M, Flores J. Transmisión interepidémica del dengue en la ciudad de Colima México. Salud pública de México. 2003; 45(5): p. 365 - 370.

  23. Esteva L, Vargas C. Coexistence of different serotypes of dengue virus. Journal of mathematical biology. 2003; 46(1): p. 31 - 47.

  24. Esteva L, Yang H. Mathematical model to assess the control of Aedes aegypti mosquitos by the sterile technique. Mathematical biosciences. 2005; 198: p. 132 - 147.

  25. Chowell G, Sánchez F. Climate-based descriptive models of dengue fever: the 2002 epidemic in colima Mexico. Journal of Environmental Health. 2008; 68(10): p. 40 - 44.

  26. Brunkard J, López J, Ramirez J, Cifuentes E, Rothenberg S, Hunsperger E, et al. Dengue Fever seroprevalence and risk factors, Texas-Mexico border, 2004. Emerging infectious diseases. 2007; 13(10): p. 1477.

  27. Chowell G, Diaz-Duenas P, Miller J, Alcazar-Velazco A, Hyman J, Fenimore P, et al. Estimation of the reproduction number of dengue fever from spatial epidemic data. Mathematical biosciences. 2007; 208(2): p. 571 - 589.

  28. Brunkard J, Cifuentes E, Rothenberg S. Assesing the roles of temperature, precipitation, and ENSO y dengue re-emergence on the Texas-Mexico border region. Salud publica de México. 2008; 50(3): p. 227 - 234.

  29. Tun‐Lin W, Lenhart A, Nam V, Rebollar‐Téllez E, Morrison A, Barbazan P, et al. Reducing costs and operational constraints of dengue vector control by tarjeting productive breeding places: a multi-country non-inferiority cluster randomized trial. Tropical Medicine & International Health. 2009; 14(9): p. 1143 - 1153.

  30. Pinho S, Ferreira C, Esteva L, Barreto F, Morato-e-Silva V, Teixeira M. Modelling the dynamnics of dengue real epidemics. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2010; 368(1933): p. 5679 - 5693.

  31. Machado-Machado EA. Assessing vulnerability to dengue fever in Mexico under global change (tesis doctoral) Worcester, Massachusetts: Clark University; 2011.

  32. Aldana O, Ortiz F, Munguía M, Gómez C. Estudio de brote epidemiológico de dengue en San Antonio el Grande Hidalgo. Enfermedades Infecciosas y Microbiología. 2011; 31(3): p. 81 - 88.

  33. Lozano-Fuentes S, Hayden M, Welsh-Rodriguez C, Ochoa-Martinez C, Tapia-Santos B, Kobylinski K, et al. The dengue virus mosquito vector Aedes aegypti at high elevation in México. irus mosquito vector Aedes aegypti at high elevation in Mexico. The American journal of tropical medicine and hygiene. 2012; 87(5): p. 902 - 909.

  34. Ruiz-Ramírez J, Hernández-Rodríguez G, González-Muñoz O. Cálculo de la magnitud final del dengue por medio del método de regresión. Salud (i) ciencia (Impresa. 2012; 19(6): p. 500 - 505.

  35. Hawks-Gutierrez C. a mathematical model of dengue dynamics based on epidemiological data (tesis de maestría): Universidad de Sonora; 2014.

  36. Torres I, Cortés D, Becker I. Dengue en México: análisis de dos décadas. Gaceta Médica de México. 2014; 150(2): p. 122 - 127.

  37. Bouzid M, Colón-González F, Lung T, Lake I, Hunter P. Climate change and emergence of vector-borne disease in Europe: case study of dengue fever. BMC public health. 2014; 14(1): p. 181.

  38. Cruz-Pacheco G, Esteva L, Vargas C. Vaccination strategies for SIR vector-transmitted diseases. Bulletin of mathematical biology. 2014; 76: p. 2073 - 2090.

  39. Reyes-Castro PA. Dynamics of dengue transmission in the arid region of sonora (tesis doctoral): The University of Arizona; 2015.

  40. Guevara-Souza M, Vallejo E. A computer simulation model of wolbachia invasion for disease vector population modification. BMC Bioinformatics. 2015; 16(1): p. 317.

  41. Campbell L, Luther C, Moo-Llanes D, Ramsey J, Danis-Lozano R, Peterson A. Climate change influences on global distributions of dengue and chikungunya virus vectors. Philosophical Transactions of the Royal Society B: Biological Sciences. 2015; 370(1665): p. 1 - 9.

  42. Martínez-Vega R, Danis-Lozano R, Diaz-Quijano F, Velasco-Hernandez J, Santos-Luna R, Roman-Perez S, et al. Peridomestic intection as a determining factor of dengue transmission. PLoS neglected tropical diseases. 2015; 9(12): p. 1 - 18.

  43. Marcelino-Salvador I. Influencia de factores socio-ambientales en la incidencia de dengue: Un modelo para Baja California Sur y un modelo general para la república mexicana, (tesis de licenciatura) Pueblas: Benemérita Universidad Autónoma de Puebla; 2016.

  44. Hernández-Suárez C, Mendoza-Cano O. Empirical evidence of the effect of school gathering on the dynamics of dengue epidemics. Global health action. 2016; 9: p. 1 - 7.

  45. Falcon J, Martínez R, Kuri P, J JR, Adams B. Day to day population movement and the management of dengue epidemics. Bulletin of mathematical biology. 2016; 78: p. 2011 - 2033.

  46. Alvarado-Castro V, Ramírez-Hernández E, Paredes-Solís S, Soberanis JL, Saldaña-Herrera V, Salas-Franco L, et al. Caracterización clínica del dengue y variables predictoras de gravedad en pacientes pediátricos en un hospital de segundo nivel en chilpancingo Guerrero, México: serie de casos. Boletín médico del Hospital Infantil de México. 2016; 73(4): p. 237 - 242.

  47. Tiga D, Undurraga E, Ramos-Castañeda J, Martínez-Vega R, Tschampl C, Shepard D. Persistent symptoms of dengue: estimates of the incremental disease and economic burden in Mexico. The American journal of tropical medicine and hygiene. 2016; 94(5): p. 1085 - 1089.

  48. Pliego-Pliego C. Análisis cualitativo y numérico de modelos matemáticos para el estudio de la interacción mosquito humano en dengue y su aplicación a la simulación, pronóstico y control de brotes (tesis doctoral) Puebla: Benemérita Universidad Autónoma de Puebla; 2017.

  49. Nava-Aguilera E, Morales-Pérez A, Balanzar-Martínez A, Rodríguez-Ramírez O, Jiménez-Alejo A, Flores-Moreno M, et al. Dengue ocurrence relations and serology cross-sectional analysis of results from the Guerrero state, Mexico, baseline for a cluster-randomised controlled trial of community mobilisation for dengue prevention. BMC Public health. 2017; 17(1): p. 435.

  50. García-Luna S. Mexican mosquitoes: overcoming barriers for dengue and zika virus infection (Doctoral dissertation) Fort Collins, Colorado: Colorado state University; 2017.

  51. González N, Núñez M, Ramos J, Velasco J. Transmission dynamics of two dengue serotypes with vaccination. Mathematical biosciences. 2017; 287: p. 54 - 71.

  52. Moreno-Banda G, Riojas H, Hurtado M, Danis R, Rothenberg S. Effects of climatic and social factors on dengue incidence in Mexican mucipalities in the state of Veracruz. Salud pública de México. 2017; 59: p. 41 - 52.

  53. Yañez-Arenas C, Rioja-Nieto R, Martín G, Dzul-Manzanilla F, Chiappa-Carrara X, Buenfil-Ávila A, et al. Characterizing environmental suitability of Aedes albopictus(Diptera:Culicidae) in Mexico based on regional and global niche models. journal of medical entomology. 2017; XX: p. 69 - 77.

  54. Báez-Hernández N, Casas M, Danis R, Velasco J. A mathematical model for dengue and chikungunya in Mexico. bioRxiv. 2017;: p. 1 - 36.

  55. Falcón-Lezama J, Santos-Luna R, Román-Pérez S, Martínez-Vega R, Herrera-Valdez M, Kuri-Morales A, et al. Analysis of spatial mobility in subjects from a dengue endemic urban location in Morelos state Mexico. PloS one. 2017; 12(2): p. 1 - 19.

  56. Laureano-Rosario A, Garcia-Rejon J, Gomez-Carro S, Farfan-Ale J, Muller-Karger F. Modelling dengue fever risk in the state of Yucatan, Mexico using regional scale satellite-derived sea surface temperature. Acta tropica. 2017; 172: p. 50- 57.

  57. Murillo-Zamora E, Medina-González A, Trujillo-Hernández B, Mendoza-Cano O, Guzmán-Esquivel J, Higareda-Almaraz M, et al. Clinical markers, associated with acute laboratory-confirmed dengue infection: results of national epidemiological surveillance system. Revista de Salud Pública. 2017; 19(6): p. 744 - 748.

  58. Serrano-Pinto V, Moreno M. Dengue hemorrhagic fever in the Nortwest of Mexico: a two-decade analysis. Revista de investigación clínica. 2017; 69: p. 152 - 158.

  59. Hussain-Alkhateeb L, Kroeger A, Olliaro P, Rocklöv J, Sewe M, Tejeda G, et al. Early warning and response system (EWARS) for dengue outbreaks: recent advancements towards widespread applications in critical settings. PloS one. 2018; 13(5): p. 1 - 14.

  60. Velázquez-Castro J, Anzo-Hernández A, Bonilla-Capilla B, Soto-Bajo M, Fraguela-Collar A. Vector-borne disease risk indexes in spatially structured populations. PLoS neglected tropical diseases. 2018; 12(2): p. 1 - 18.

  61. Pliego E, Velázquez-Castro J, Eichhorn M, Collar A. Increased efficiency in the second-hand tire trade provides opportunity for dengue control. Journal of theoretical biology. 2018; 437: p. 126 - 136.

  62. Sánchez-González G, Condé R, Noguez R, López P. Prediction of dengue outbreaks in Mexico based on entomological, meteorological and demographic data. PLOS ONE. 2018; 13(8): p. 1-14.

  63. Pavía-Ruz N, Rojas DP, Villanueva S, Granja P, Balam-May A, Longini IM, et al. Seroprevalence of dengue antibodies in three urban settings in Yucatan Mexico. The American Society of Tropical Medicine and Hygiene. 2018; 98(4): p. 1202 - 1208.

  64. Ortigoza G, Brauer F, Lorandi A. Mosquito-borne diseases simulated by cellular automata: A review. International Journal of Mosquito Research. 2019; 6(6): p. 21 - 38.




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