Advertisement

Environmental and Ecological Statistics

, Volume 26, Issue 1, pp 1–16 | Cite as

Modeling Aedes aegypti trap data with unobserved components

  • Thiago Rezende dos SantosEmail author
Article

Abstract

Several models have been proposed to describe the population dynamics of Aedes aegypti. Intuitive interpretation of model parameters and simplicity are some of the main characteristics of mechanistic models. Another possibility is the use of statistical models, which have their advantages but are not easy to interpret. The state-space model (SSM), also known as a mechanistic time series model, incorporates the beneficial aspects of both mechanistic and statistical models. This study introduces a SSM for Ae. aegypti ovitrap data to estimate latent state and static parameters, making suitable analysis of the data. The estimation of static and state parameters is easy to achieve in this framework. A simulation study is performed to study some properties of the estimators for the parameters. The model is also applied to Ae. aegypti trap data and highlights its importance and potential for the real trap data sets. The results show that the proposed SSM has good performance and the parameters can be reasonably estimated.

Keywords

Classical inference Dengue Ovitraps State-space models Time series 

Notes

Acknowledgements

T. R. Santos was supported by the PrPq-Universidade Federal de Minas Gerais-Brazil, CNPq-Brazil, and the FAPEMIG Foundation. The author thanks the associate editor and two anonymous reviewers for constructive comments and suggestions which substantially helped improve the quality of the paper. The author also thanks Helio Eustaquio dos Santos (in memoriam), Alzira de Rezende dos Santos, and Graciele Fernanda for their endless discussions.

References

  1. Barsante LS, Paixao KS, Laass KH, Cardoso RTN, Eiras AE, Acebal JL (2014) A model to predict the population size of the dengue fever vector based on rainfall data. arXiv preprint arXiv:1409.7942
  2. Bonat WH, Ribeiro PJ Jr, Krainski ET (2014) Modelagem espaço-temporal de contagens de ovos de Aedes aegypti em Recife-PE. Rev Bras Estat 74:75–100Google Scholar
  3. Bretó C, He D, Ionildes EL, King AA (2009) Time series analysis via mechanistic models. Ann Appl Stat 3(1):319–348CrossRefGoogle Scholar
  4. Cardoso Junior RP, Scandar SAS, Mello NVD, Ernandes S, Botti MV, Nascimento EM (1997) Detecção de Aedes aegypti e Aedes albopictus, na zona urbana do município de Catanduva-SP, após controle de epidemia de dengue. Rev Soc Bras Med Trop 30(1):37–40CrossRefGoogle Scholar
  5. Chen S, Frics J, Ferrari MJ (2012) Tracking measles infection through non-linear state space models. J R Stat Soc Ser C (Appl Stat) 61(1):117–134CrossRefGoogle Scholar
  6. Codeço CT, Lima AW, Araújo SC, Lima JBP, Maciel-de-Freitas R, Honório NA, Valle D (2015) Surveillance of Aedes aegypti: comparison of house index with four alternative traps. PLoS Negl Trop Dis 9(2):e0003475–e0003475CrossRefGoogle Scholar
  7. De Almeida PS, Meotti C, Dos Santos Almeida G, Nascimento J, De Araujo AD, Faccenda O, Gino M (2013) Infestação de Aedes aegypti (Linnaeus, 1762)(diptera: culicidae) determinada por armadilhas de oviposição (ovitrampas) no município de Costa Rica, estado de Mato Grosso do Sul. Rev Patol Trop 42(3):331–339CrossRefGoogle Scholar
  8. Doornik JA (1999) Ox: an object-oriented matrix language, 3rd edn. Timberlake Consultants Press, LondonGoogle Scholar
  9. Dukic V, Lopes HF, Polson NG (2012) Tracking epidemics with Google flu trends data and a state-space SEIR model. J Am Stat Assoc 107(500):1410–1426CrossRefGoogle Scholar
  10. Dye C (1984) Competition amongst larval Aedes aegypti: the role of interference. Ecol Entomol 9(3):355–357CrossRefGoogle Scholar
  11. Estallo EL, Ludueña-Almeida FF, Visitin AM, Scavuzzo CM, Introini MV, Zaidenberg M, Almirón WR (2011) Prevention of dengue outbreaks through Aedes aegypti oviposition activity forecasting method. Vector Borne Zoonotic Dis 11:543–549CrossRefGoogle Scholar
  12. Estallo EL, Ludueña-Almeida FF, Visitin AM, Scavuzzo CM, Lamfri MA, Introini MV, Zaidenberg M, Almirón WR (2012) Effectiveness of normalized difference water index in modeling Aedes aegypti house index. Int J Remote Sens 33:4254–4265CrossRefGoogle Scholar
  13. Estallo EL, Ludueña-Almeida FF, Introini MV, Zaidenberg M, Almirón WR (2015) Weather variability associated with Aedes (Stegomyia) aegypti (Dengue vector) oviposition dynamics in Northwestern Argentina. PLOS ONE 10:1–11CrossRefGoogle Scholar
  14. Esteva L, Vargas C (1998) Analysis of a dengue disease transmission model. Math Biosci 100(2):131–151CrossRefGoogle Scholar
  15. Ferreira CP, Yang HM (2003) Estudo Dinâmico da População de Mosquito Aedes aegypti. Tend Mat Apl Comput 4:187–196Google Scholar
  16. Focks DA, Haile DG, Daniels E, Mount GA (1993) Dynamic life table model for Aedes aegypti (Diptera: Culicidae): simulation results and validation. J Med Entomol 30(6):1018–1028CrossRefGoogle Scholar
  17. Gamerman D, Santos TR, Franco GC (2013) A non-Gaussian family of state-space models with exact marginal likelihood. J Time Ser Anal 34:625–645CrossRefGoogle Scholar
  18. Harvey AC (1989) Forecasting, structural time series models and the Kalman filter. University Press, CambridgeGoogle Scholar
  19. Honório NA, Codeço CT, Alves FC, Magalhães MDAFM, Lourenço-de-Oliveira R (2009) Temporal distribution of Aedes aegypti in different districts of Rio de Janeiro, Brazil, measured by two types of traps. J Med Entomol 46(5):1001–1014CrossRefGoogle Scholar
  20. IBGE (2010) Instituto Brasileiro de Geografia e Estatistica, Ministerio do Planejamento, Orcamento e Gestao. http://www.ibge.gov.br/estadosat/perfil.php?sigla=ms. Accessed 25 May 2018
  21. Kalman RE (1960) A new approach to linear filtering and prediction problems. J Fluids Eng 82(1):35–45Google Scholar
  22. Lana RM, Carneiro TG, Honório NA, Codeço CT (2011) Multiscale analysis and modelling of Aedes aegypti population spatial dynamics. J Inf Data Manag 2(2):211–220Google Scholar
  23. Lana RM, Carneiro TG, Honório NA, Codeço CT (2014) Seasonal and nonseasonal dynamics of Aedes aegypti in Rio de Janeiro, Brazil: fitting mathematical models to trap data. Acta Trop 129:25–32CrossRefGoogle Scholar
  24. Nobre FF, Monteiro ABS, Telles PR, Williamson GD (2001) Dynamic linear model and SARIMA: a comparison of their forecasting performance in epidemiology. Stat Medi 20(20):3051–3069CrossRefGoogle Scholar
  25. Otero M, Solari HG, Schweigmann N (2006) A stochastic population dynamics model for Aedes aegypti: formulation and application to a city with temperate climate. Bull Math Biol 68(8):1945–1974CrossRefGoogle Scholar
  26. Otero M, Schweigmann N, Solari HG (2008) A stochastic spatial dynamical model for Aedes aegypti. Bull Math Biol 70(5):1297–1325CrossRefGoogle Scholar
  27. R Core Team (2013) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. http://www.R-project.org/. Accessed 13 January 2017
  28. Resende MCD, Silva IM, Ellis BR, Eiras AE (2013) A comparison of larval, ovitrap and MosquiTRAP surveillance for Aedes (Stegomyia) aegypti. Mem Inst Oswaldo Cruz 108(8):1024–1030CrossRefGoogle Scholar
  29. Santos TR, Franco GC (2019) Bootstrap for correcting the mean square error of prediction and smoothed estimates in structural models. Braz J Probab Stat (forthcoming)Google Scholar
  30. Shanno DF (1970) Conditioning of quasi-Newton methods for function minimization. Math Comput 24:647–656CrossRefGoogle Scholar
  31. Simões TC, Codeço CT, Nobre AA, Eiras AE (2013) Modeling the non-stationary climate dependent temporal dynamics of Aedes aegypti. PloS one 8(8):e64773CrossRefGoogle Scholar
  32. Wang J, Liang H, Chen R (2012) A state space model approach for HIV infection dynamics. J Time Ser Anal 33(5):841–849CrossRefGoogle Scholar
  33. West M, Harrison J (1997) Bayesian forecasting and dynamic models. Springer, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of StatisticsUniversidade Federal de Minas GeraisBelo HorizonteBrazil

Personalised recommendations