
Mathematical Biosciences and Engineering, 2019, 16(6): 82178242. doi: 10.3934/mbe.2019416
Research article
Export file:
Format
 RIS(for EndNote,Reference Manager,ProCite)
 BibTex
 Text
Content
 Citation Only
 Citation and Abstract
Estimation of the expected number of cases of microcephaly in Brazil as a result of Zika
Department of Mathematics and Statistics, University of Strathclyde, Glasgow, G1 1XH, UK
Received: , Accepted: , Published:
We have estimated the value of the basic reproduction number for Zika in Brazil and calculated the expected number of cases of microcephaly in newborns as a result of women infected with Zika during pregnancy. We started off with a nonagestructured model then introduced agestructure into the model.
However in reality seasonality, in particular temperature and rainfall, have a great impact on the population size of A. aegypti. Hence we repeat both the nonagestructured and agestructured analyses introducing seasonality into the A. aegypti birth function to model the effect of these environmental factors.
References
1. E. Massad, F. A. B. Coutinho, M. N. Burattini, et al., Estimation of R_{0} from the initial phase of an outbreak of a vectorborne infection, Trop. Med. Int. Health, 15 (2010), 120126.
2. G. Adamu, M. Bawa, M. Jiya, et al., A mathematical model for the dynamics of Zika virus via homotopy perturbation method, J. Appl. Sci. Environ. Manage., 21 (2017), 615623.
3. E. Bonyah and K. O. Okosun, Mathematical modeling of Zika virus, Asian Pac. J. Trop. Dis., 6 (2016), 673679.
4. C. Ding, N. Tao and Y. Zhu, A mathematical model of Zika virus and its optimal control, In Proc. of the 35th CCC Conf., 2016, Chengdu, China, (2016), 26422645.
5. G. GonzálezParra and T. Benincasa, Mathematical modeling and numerical simulations of Zika in Colombia considering mutation, Math. Comput. Simul., 163 (2019), 18.
6. N. K. Goswami, A. K. Srivastav, M. Ghosh, et al., Mathematical modeling of Zika virus disease with nonlinear incidence and optimal control, in J. Phys. Conf. Ser., 1000 (2018), 116.
7. B. Mahatoa and B. K. Mishrab, Global stability analysis on the transmission dynamics of Zika virus, Int. J. Appl. Eng. Res., 13 (2018), 1229612303.
8. S. C. Mpeshe, N. Nyerere and S. Sanga, Modeling approach to investigate the dynamics of Zika virus fever: a neglected disease in Africa, Int. J. Adv. Appl. Math. Mech. 4 (2017), 1421.
9. F. Ndairou, I. Area, J. J. Nieto, et al., Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil, Math. Meth. Appl. Sci. 41 (2018), 89298941.
10. T. O. Oluyo and M. O. Adeyemi, Mathematical analysis of Zika epidemic model, IOSR J. Math., 12 (2016), 2133.
11. B. Tang, Y. Xiao and J. Wu, Implication of vaccination against dengue for Zika outbreak, Sci. Rep., 6 (2016), article number 35623.
12. B. Tang, W. Zhou, Y. Xiao, et al., Implication of sexual transmission of Zika on dengue and Zika outbreaks, Math. Biosci. Eng., 16 (2019), 50925113.
13. N. M. Ferguson, Z. M. Cucunubá, I. Dorigatti, et al., Countering the Zika epidemic in Latin America, Science, 353 (2016), 353354.
14. M. Andraud, N. Hens, C. Marais, et al., Dynamic epidemiological models for dengue transmission: a systematic review of structural approaches, PLoS One, 7 (2012), p.e49085.
15. E. Chikak and H. Ishikawa, A dengue transmission model in Thailand considering sequential infections with all four serotypes, J. Infect. Dev. Countr., 3 (2009), 711722.
16. World Health Organization. Countries: Brazil, 2017. Available from: http://www.who.int/countries/bra/en/.
17. Centers for Disease Control and Prevention, Surveillance and control of Aedes aegypti and Aedes albopictus in the United States, 2017. Available from: https://www.cdc.gov/chikungunya/resources/vectorcontrol.html.
18. D. Focks, N. Alexander and E. Villegas, Multicountry study of Aedes aegypti pupal productivity survey methodology: findings and recommendations, UNICEF/UNDP/World Bank/WHO Special Programme for Research and Training in Tropical Disease (TDR), 2006. Available from: http://www.who.int/tdr/publications/documents/aedes_aegypti.pdf.
19. E. Massad, F. A. B. Coutinho, M. N. Burattini, et al., The risk of yellow fever in a dengueinfested area, Trans. R. Soc. Trop. Med. Hyg., 95 (2001), 370374.
20. G. Chowell, R. Fuentes, A. Olea, et al., The basic reproduction number R_{0} and effectiveness of reactive interventions during dengue epidemics: The 2002 dengue outbreak in Easter Island, Chile, Math. Biosci. Eng., 10 (2013), 14551474.
21. A. K. Supriatna, Estimating the basic reproduction number of dengue transmission during 2002 2007 outbreaks in Bandung, Indonesia, WHO Regional Office for SouthEast Asia. Dengue Bulletin, 33 (2009), 2133. Available from: http://www.who.int/iris/handle/10665/170937.
22. S. Cauchemez, M. Besnard, P. Bompard, et al., Association between Zika virus and microcephaly in French Polynesia, 20132015: a retrospective study, The Lancet, 387 (2016), 21252132.
23. M. A. Johansson, L. MieryTeranRomero, J. Reefhuis, et al., Zika and the risk of of microcephaly, N. Engl. J. Med., 375 (2016), 14.
24. United Nations, United Nations, department of economic and social affairs, population division. World population prospects: The 2015 revision, (2015). Available from: https://esa.un.org/unpd/wpp/Graphs/DemographicProfiles/.
25. H. Nishiura, K. Mizumoto, K. S. Rock, et al., A theoretical estimate of the risk of microcephaly during pregnancy, Epidemics, 15 (2016), 6670.
26. J. LiuHelmersson, H. Stenlund, A. WilderSmith, et al., Vectorial capacity of Aedes aegypti: effects of temperature and implications for global dengue epidemic potential, PLoS One, 9 (2014), e89783.
27. H. S. Rodrigues, M. T. Monteiro and D. M. Torres, Seasonality effects on dengue: basic reproduction number, sensitivity analysis and optimal control, Math. Meth. Appl. Sci., 39 (2016), 46714679.
28. S. Wiwanitkit and V. Wiwanitkit, Predicted pattern of Zika virus infection distribution with reference to rainfall in Thailand, Asian Pac. J. Trop. Med., 9 (2016), 719720.
29. A. G. Barnett, P. Baker and A. J. Dobson, Analysing seasonal data, The R Journal, 4 (2012). Available from: https://journal.rproject.org/archive/2012/RJ2012001/RJ2012001.pdf.
30. M. N. Burattini, M. Chen, A. Chow, et al., Modelling the control strategies against dengue in Singapore, Epidemiol. Infect., 136 (2008), 309319.
31. N. M. Ferguson, Z. M. Cucunubá, I. Dorigatti, et al., Supplementary materials for countering the Zika epidemic in Latin America, 2016. Available from: www.sciencemag.org/content/353/6297/353/suppl/DC1.
32. E. Massad, F. A. B. Coutinho, L. F. Lopez, et al., Modelling the impact of global warming on vectorborne infections, Phys. Life Rev., 8 (2011), 169199.
33. H. S. Rodrigues, M. T. Monteiro and D. M. Torres, Seasonality effects on dengue, In Proc. of the 14th CMMSE Conf. Costa Ballena, Rota, Cadiz, Spain, 2014, (2014), 10841091.
34. A. M. Stolwijk, H. Straatman and G. A. Zielhuis, Studying seasonality by using sine and cosine functions in regression analysis, J. Epidemiol. Commun. Health, 53 (1999), 235238.
35. Pan American Health Organization/World Heath Organization, Zikaepidemiological report Brazil. Washington, D.C: PAHO/WHO, 2017.
36. B. Haynes and A. Boadle, Brazil says Zikalinked microcephaly cases stable at 4,908, Health News, 2016. Available from http://www.reuters.com/article/ushealthzikabrazilidUSKCN0XN2NP.
37. T. V. de Araújo, L. C. Rodrigues, R. A. de Alencar Ximenes, et al., Association between Zika virus infection and microcephaly in Brazil, January to May, 2016: preliminary report of a casecontrol study, The Lancet Infect. Dis., 16 (2016), 13561363.
38. F. B. Agusto, A. B. Gumel and P. E. Parham, Qualitative assessment of the role of temperature variations in malaria transmission dynamics, J. Biol. Syst., 23 (2015), 597630.
39. O. Koutou, B. Traoré and B. Sangoré, Mathematical modelling of malaria transmission global dynamics taking into account the immature stages of the vectors, Adv. in Differ. Equ., 2018, 220.
40. L. Coudeville and G. P. Garnett, Transmission dynamics of the four dengue serotypes in Southern Vietnam and the potential impact of vaccination, PLoS One, 7 (2012), e51244.
41. S. B. Maier, X. Huang, E. Massad, et al., Analysis of the optimal age for dengue vaccination in Brazil with a tetravalent dengue vaccine, Math. Biosci., 294 (2017), 1532.
42. D. Gao, Y. Lou, D. He, et al., Prevention and control of Zika as a mosquitoborne and sexually transmitted disease: a mathematical modeling analysis, Sci. Rep., 6 (2016), Article Number 28070.
43. L. Wang, H. Zhao, S. M. Oliva, et al., Modelling the transmission and control of Zika in Brazil, Sci. Rep., 7 (2017), article number 7721.
44. M. Amaku, M. N. Burattini, F. A. B. Coutinho, et al., Estimating the size of the HCV infection prevalence: a modelling approach using the incidence of cases reported to an official notification system, Bull. Math. Biol., 78 (2016), 970990.
45. M. Amaku, M. N. Burattini, E. Chaib, et al., Estimating the prevalence of infectious diseases from underreported agedependent compulsorily notification databases, Theor. Biol. Med. Model., 14 (2017), 23.
46. P. S. Mead, N. K. Duggal, S. A. Hook, et al., Zika virus shedding in semen of symptomatic infected men, N. Engl. J. Med., 378 (2018), 13771385.
47. M. Zamani and V. Zamani, Sexual transmission of Zika virus: an assessment of the evidence, Iran. J. Public Health, 46 (2017), 13051306.
48. R. Lowe, C. Barcellos, P. Brasil, et al., The Zika virus epidemic in Brazil: from discovery to future implications, Int. J. Environ. Res. Public Health, 15 (2018), E96.
49. A. J. Kucharski, S. Funk, R. M. Eggo, et al., Transmission dynamics of Zika virus in island populations: a modelling analysis of the 201314 French Polynesia outbreak, PLoS Negl. Trop. Dis., 10 (2016), e0004726.
50. S. Funk, A. J. Kucharski, A. Camacho, et al., Comparative analysis of dengue and Zika outbreaks reveals differences by setting and virus, PLoS Negl. Trop. Dis., 10 (2016), e0005173.
51. M. S. Majumder, M. Santillana, S. R. Mekaru, et al., Utilizing nontraditional data sources for realtime estimation of transmission dynamics during the 20152016 Colombian Zika virus disease outbreak, JMIR Public Health Surveill., 2 (2016), e30
© 2019 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)