Modeling of Infectious Diseases: A Core Research Topic for the Next Hundred Years

  • I Gede Nyoman Mindra JayaEmail author
  • Henk Folmer
  • Budi Nurani Ruchjana
  • Farah Kristiani
  • Yudhie Andriyana
Part of the Advances in Spatial Science book series (ADVSPATIAL)


Incidence of infectious diseases is an under-researched topic in regional science. This situation is unfortunate because the occurrence of these types of diseases frequently has far-reaching welfare impacts at household, regional, national, and even international levels. Given its welfare impacts and soaring incidence, inter alia, because of climate change, increasing population density, higher mobility, and increasing immunity to several common medicines, the occurrence and spread of infectious diseases should become a regular research topic in regional science. There are also methodological reasons why regional scientists should pay (more) attention to the incidence of infectious diseases. Although both regional science and epidemiology deal with the spatial distributions of their research topics and apply spatial analytical techniques, important methodological differences between them open possibilities for cross-fertilization. This study presents an overview of the main models and estimators of infectious disease incidence. We first discuss maximum likelihood (ML), which is the most common estimator. It is unbiased but imprecise and unreliable for small regions. Next we discuss several methods that have been proposed to improve ML estimation by smoothing (i.e., Bayesian smoothing techniques and nonparametric estimators). From the review, we conclude that none of the models used so far adequately considers the most basic characteristic of infectious diseases, namely, spatial spillover. We argue that the development and application of infectious disease models that allow for spatial spillover is a core research topic for the years to come. We conclude the chapter with suggestions for future regional science research themes in the area of infectious diseases.


Disease modeling Maximum likelihood Bayesian smoothing Non-parametric estimation Spatial spillover 


  1. Ando AW, Baylis K (2013) Spatial environmental and natural resource economics. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer, New York, pp 1029–1048Google Scholar
  2. Anselin L, Lozano N, Koschinsky J (2006) Rate transformations and smoothing. University of Illinois, UrbanaGoogle Scholar
  3. Bernardinelli L et al (1995) Bayesian analysis of space-time variation in disease risk. Stat Med 14:2433–2443CrossRefGoogle Scholar
  4. Besag J, York J, Mollié A (1991) Bayesian image restoration with two applications in spatial statistics. Ann Inst Stat Math 43:1–59CrossRefGoogle Scholar
  5. Bivand RS, Gómez-Rubio V, Rue H (2014) Approximate bayesian inference for spatial econometrics models. Spatial Statistics 9:146–165CrossRefGoogle Scholar
  6. Chen D, Moulin B, Wu J (2015) Sntroduction to analyzing and modeling spatial and temporal dynamics of infectious diseases. In: Chen D, Moulin B, Wu J (eds) Analyzing and modeling spatial and temporal dynamics of infectious diseases. Wiley, Hoboken, NJ, pp 3–17Google Scholar
  7. Clayton D, Kaldor J (1987) Empirical bayes estimates of age-standardized relative risks for use in disease mapping. Biometrics 43(3):671–681CrossRefGoogle Scholar
  8. Congdon P (2010) Bayesian hierarchical method. Tylor & Francis Group, New YorkCrossRefGoogle Scholar
  9. Congdon P (2013) Bayesian spatial statistical modeling. In: Fischer MM, Nijkamp P (eds) Handbook of regional science. Springer, New York, pp 1419–1434Google Scholar
  10. Fong I (2013) Emerging infectious diseases of the 21st century, challenges in infectious diseases. Springer, TorontoGoogle Scholar
  11. Hog RV, McKean JW, Craig AT (2005) Introduction to mathematical statistics. Pearson Prentice Hall, Upper Saddle River, NJGoogle Scholar
  12. Kesall JE, Diggle PJ (1998) Spatial variation in risk of disease: a nonparametric binary regression approach. Appl Stat 47(2):559–573Google Scholar
  13. Lambert DM, Brown JP, Florax RJ (2010) A two-step estimator for a spatial lag model of counts: theory, small sample performance and an application. Reg Sci Urban Econ 40(4):241–252CrossRefGoogle Scholar
  14. Lawson AB (2006) Statistical methods methods in spatial epidemiology. Wiley, ChichesterCrossRefGoogle Scholar
  15. Lawson AB (2013) Bayesian disease mapping, hierarchical modeling in spatial epidemiology, 2nd edn. CRC Press/Taylor & Francis Group, Boca Raton, FLGoogle Scholar
  16. Lawson AB (2014) Hierarchical modeling in spatial WIREs. Comput Stat. doi: 10.1002/wics.1315 Google Scholar
  17. Lawson AB, Biggeri B et al (2000) Disease mapping models: an empirical evaluation. Stat Med 19:2217–2241CrossRefGoogle Scholar
  18. Lawson AB, Browne WJ, Rodeiro CL (2003) Disease mapping with WinBUGS and MLwiN. Wiley, ChichesterCrossRefGoogle Scholar
  19. Lee D (2013) CARBayes: an R package for bayesian spatial modeling with conditional autoregressive priors. J Stat Softw 55(13):1–24CrossRefGoogle Scholar
  20. Leonard T (1975) Bayesian estimation methods for two-way contingency tables. J R Stat Soc ser B 37:23–37Google Scholar
  21. Leroux B, Lei X, Breslow N (1999) Estimation of disease rates in small areas: a new mixed model for spatial dependence. In: Halloran ME, Berry D (eds) Statistical models in epidemiology, the environment, and clinical trials. Springer, New York, pp 135–178Google Scholar
  22. Lowe R, Bailey TC, Stephenson DB et al (2011) Spatiotemporal modeling of climate-sensitive disease risk: towards an early warning system for dengue in Brazil. Comput Geosci 37:371–381CrossRefGoogle Scholar
  23. MacNab YC, Dean C (2002) Spatiotemporal modeling of rates for the construction of disease maps. Stat Med 21:347–358CrossRefGoogle Scholar
  24. Maiti T (1998) Hierarchical bayes estimation of mortality rates disease mapping. J Stat Plan Inference 69(2):339–348CrossRefGoogle Scholar
  25. Martinez EZ, Achcar AJ (2014) Trends in epidemiology in the 21st century: time to adopt Bayesian methods. Cad Saúde Pública 30(4):703–714CrossRefGoogle Scholar
  26. Meza JL (2003) Empirical bayes estimation smoothing of relative risks in disease mapping. J Stat Plan Inference 11:43–62CrossRefGoogle Scholar
  27. Pringle D (1996) Mapping disease risk estimates based on small number :an assessment of empirical bayes techniques. Econ Soc Rev 27(4):341–363Google Scholar
  28. Rao J (2003) Small area estimation. Wiley, OttawaCrossRefGoogle Scholar
  29. Rue H, Martino S, Chopin N (2007) Approximate bayesian inference for latent gaussian models using integrated nested laplace approximations. Statistics Report No 1. Norwegian University of Science and TechnologyGoogle Scholar
  30. Shaddick G, Zidek JV (2016) Spatiotemporal methods in environmental epidemiology. CRC Press/Taylor & Francis Group, New YorkGoogle Scholar
  31. Simonoff JS (1999) Smoothing methods in statistics. Springer, New YorkGoogle Scholar
  32. Stern H, Cressie N (1999) Inference for extremes in disease mapping. In: Lawson AB, Biggeri A, Bohning D et al (eds) Disease mapping and risk assessment for public health. Wiley, New York, pp 63–84Google Scholar
  33. Tango T (2010) Statistical methods for disease clustering theory and methods. Springer, LondonCrossRefGoogle Scholar
  34. WHO (2005) Using climate to predict infectious disease epidemics. WHO, GenevaGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • I Gede Nyoman Mindra Jaya
    • 1
    Email author
  • Henk Folmer
    • 2
  • Budi Nurani Ruchjana
    • 3
  • Farah Kristiani
    • 4
  • Yudhie Andriyana
    • 1
  1. 1.Statistics DepartmentUniversitas PadjadjaranKabupaten SumedangIndonesia
  2. 2.Faculty of Spatial ScienceUniversity of GroningenGroningenThe Netherlands
  3. 3.Mathematics DepartmentUniversitas PadjadjaranKabupaten SumedangIndonesia
  4. 4.Mathematics DepartmentParahyangan Catholic UniversityKota BandungIndonesia

Personalised recommendations