A Compartmental Model for Meningitis: Separating Transmission From Climate Effects on Disease Incidence

Article

Abstract

The timing and size of many infectious disease outbreaks depend on climatic influences. Meningitis is an example of such a disease. Every year countries in the so-called African meningitis belt are afflicted with meningococcal meningitis disease outbreaks. The timing of these outbreaks coincide with the dry season that starts in February and ends in late May. There are two main hypotheses about this strong seasonal effect. The first hypothesis assumes that during the dry season there is an increase in the risk that an individual will transition from being an asymptomatic carrier to having invasive disease. The second hypothesis states that the incidence of meningitis increases due to higher transmission of the infection during the dry season. These two biological hypotheses suggest dynamics that would necessitate different public health responses: the first would result in broadly correlated outbreak dynamics, and thus a regional vaccination response; the second would result in locally correlated outbreaks, spreading from location to location, for which a localized response may be effective in containing regional spread. In this paper, we develop a statistical model to investigate these hypotheses. Easily interpretable parameters of the model allow us to study and compare differences in the attack rates, rates of transmission and the possible underlying environmental effect during the dry and non-dry seasons. Standard maximum likelihood or Bayesian inference for this model is infeasible as there are potentially tens of thousands of latent variables in the model and each evaluation of the likelihood is expensive. We therefore propose an approximate Bayesian computation (ABC) approach to infer the unknown parameters. Using simulated data examples, we demonstrate that it is possible to learn about some of the important parameters of our model using our methodology. We apply our modeling and inferential approach to data on cases of meningitis for 34 communities in Nigeria from Medecins Sans Frontières (MSF) and World Health Organization (WHO) for 2009. For this particular data set we are able to find weak evidence in favor of the first hypothesis, suggesting a regional vaccination response.

Key Words

Approximate Bayesian computation Climate effects on disease Compartmental model Disease dynamics Meningitis Space–time model 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Beaumont, M., Zhang, W., and Balding, D. (2002), “Approximate Bayesian Computation in Population Genetics,” Genetics, 162 (4), 2025. Google Scholar
  2. Brundage, J., and Zollinger, W. (1987), “Evolution of Meningococcal Disease Epidemiology in the US Army,” in Evolution of Meningococcal Disease, Vol. 1, Boca Raton: CRC Press, pp. 5–25. Google Scholar
  3. Chen, M.-H., Shao, Q.-M., and Ibrahim, J. G. (2000), Monte Carlo Methods in Bayesian Computation, Berlin: Springer. MATHCrossRefGoogle Scholar
  4. Cookson, S., Corrales, J., Lotero, J., Regueira, M., Binsztein, N., Reeves, M., Ajello, G., and Jarvis, W. (1998), “Disco Fever: Epidemic Meningococcal Disease in Northeastern Argentina Associated with Disco Patronage,” The Journal of Infectious Diseases, 178 (1), 266. CrossRefGoogle Scholar
  5. Didelot, X., Everitt, R., Johansen, A., and Lawson, D. (2010), “Likelihood-Free Estimation of Model Evidence,” Bayesian Analysis, 6 (1), 49–76. MathSciNetCrossRefGoogle Scholar
  6. Fearnhead, P., and Prangle, D. (2010), “Constructing summary statistics for approximate Bayesian computation: Semi-automatic abc.” Google Scholar
  7. Fischer, M., Hedberg, K., Cardosi, P., Plikaytis, B., Hoesly, F., Steingart, K., Bell, T., Fleming, D., Wenger, J., and Perkins, B. (1997), “Tobacco Smoke as a Risk Factor for Meningococcal Disease,” The Pediatric Infectious Disease Journal, 16 (10), 979. CrossRefGoogle Scholar
  8. Flegal, J., Haran, M., and Jones, G. (2008), “Markov Chain Monte Carlo: Can We Trust the Third Significant Figure,” Statistical Science, 23 (2), 250–260. MathSciNetCrossRefGoogle Scholar
  9. Francois, O., and Laval, G. (2011), “Deviance Information Criteria for Model Selection in Approximate Bayesian Computation,” Statistical Applications in Genetics and Molecular Biology, 10 (1), 33. MathSciNetCrossRefGoogle Scholar
  10. Greenwood, B. (1999), “Meningococcal Meningitis in Africa,” Transactions of the Royal Society of Tropical Medicine and Hygiene, 93 (4), 341–353. MathSciNetCrossRefGoogle Scholar
  11. — (2006), “Editorial: 100 Years of Epidemic Meningitis in West Africa—Has Anything Changed?” Tropical Medicine and International Health, 11 (6), 773–780. MathSciNetCrossRefGoogle Scholar
  12. Greenwood, B., Bradley, A., Cleland, P., Haggie, M., Hassan-King, M., Lewis, L., Macfarlane, J., Taqi, A., Whittle, H., and Bradley-Moore, A. et al. (1979), “An Epidemic of Meningococcal Infection at Zaria, Northern Nigeria. 1. General Epidemiological Features,” Transactions of the Royal Society of Tropical Medicine and Hygiene, 73 (5), 557–562. CrossRefGoogle Scholar
  13. Harrison, L., Trotter, C., and Ramsay, M. (2009), “Global Epidemiology of Meningococcal Disease,” Vaccine, 27, B51–B63. CrossRefGoogle Scholar
  14. Imrey, P., Jackson, L., Ludwinski, P., England, A., Fella, G., and Fox, B. et al. (1996), “Outbreak of Serogroup C Meningococcal Disease Associated with Campus Bar Patronage,” American Journal of Epidemiology, 143 (6), 624. CrossRefGoogle Scholar
  15. Jones, G., Haran, M., Caffo, B., and Neath, R. (2006), “Fixed-Width Output Analysis for Markov Chain Monte Carlo,” Journal of the American Statistical Association, 101 (476), 1537–1547. MathSciNetMATHCrossRefGoogle Scholar
  16. Kass, R., and Raftery, A. (1995), “Bayes Factors,” Journal of the American Statistical Association, 90, 773–795. MATHCrossRefGoogle Scholar
  17. Keeling, M., and Rohani, P. (2008), “Modeling Infectious Diseases in Humans and Animals,” Clinical Infectious Diseases, 47, 864–866. CrossRefGoogle Scholar
  18. Kristiansen, P., Diomande, F., Wei, S., Ouedraogo, R., Sangare, L., Sanou, I., Kandolo, D., Kabore, P., Clark, T., and Ouedraogo, A. et al. (2011), “Baseline Meningococcal Carriage in Burkina Faso Before the Introduction of a Meningococcal Serogroup a Conjugate Vaccine,” Clinical and Vaccine Immunology, 18 (3), 435. CrossRefGoogle Scholar
  19. Lapeyssonnie, L. (1963), La méningite cérébro-spinale en Afrique, Geneva: Organisation mondiale de la santé. Google Scholar
  20. Marjoram, P., Molitor, J., Plagnol, V., and Tavaré, S. (2003), “Markov Chain Monte Carlo Without Likelihoods,” Proceedings of the National Academy of Sciences of the United States of America, 100 (26), 15324. CrossRefGoogle Scholar
  21. McKinley, T., Cook, A., and Deardon, R. (2009), “Inference in Epidemic Models Without Likelihoods,” The International Journal of Biostatistics, 5 (1), 24. MathSciNetCrossRefGoogle Scholar
  22. Molesworth, A., Cuevas, L., Connor, S., Morse, A., and Thomson, M. (2003), “Environmental Risk and Meningitis Epidemics in Africa,” Emerging Infectious Diseases, 9 (10), 1287. CrossRefGoogle Scholar
  23. Molesworth, A., Thomson, M., Connor, S., Cresswell, M., Morse, A., Shears, P., Hart, C., and Cuevas, L. (2002), “Where Is the Meningitis Belt? Defining an Area at Risk of Epidemic Meningitis in Africa,” Transactions of the Royal Society of Tropical Medicine and Hygiene, 96 (3), 242–249. CrossRefGoogle Scholar
  24. Mueller, J., and Gessner, B. (2010), “A Hypothetical Explanatory Model for Meningococcal Meningitis in the African Meningitis Belt,” International Journal of Infectious Diseases, 14 (7), e553–e559. CrossRefGoogle Scholar
  25. Pritchard, J., Seielstad, M., Perez-Lezaun, A., and Feldman, M. (1999), “Population Growth of Human Y Chromosomes: a Study of Y Chromosome Microsatellites,” Molecular Biology and Evolution, 16 (12), 1791. CrossRefGoogle Scholar
  26. Ratmann, O., Jørgensen, O., Hinkley, T., Stumpf, M., Richardson, S., and Wiuf, C. (2007), “Using Likelihood-Free Inference to Compare Evolutionary Dynamics of the Protein Networks of H. Pylori and P. Falciparum,” PLoS Computational Biology, 3 (11), e230. CrossRefGoogle Scholar
  27. Ryan, K. J., and Ray, C. G. (2004), Sherris Medical Microbiology: an Introduction to Infectious Diseases, New York: McGraw-Hill Medical. Google Scholar
  28. Sultan, B., Labadi, K., Guégan, J., and Janicot, S. (2005), “Climate Drives the Meningitis Epidemics Onset in West Africa,” PLoS Medicine, 2 (1), e6. CrossRefGoogle Scholar
  29. Tappero, J., Reporter, R., Wenger, J., Ward, B., Reeves, M., Missbach, T., Plikaytis, B., Mascola, L., and Schuchat, A. (1996), “Meningococcal Disease in Los Angeles County, California, and Among Men in the County Jails,” The New England Journal of Medicine, 335 (12), 833. CrossRefGoogle Scholar
  30. Thomson, M., Molesworth, A., Djingarey, M., Yameogo, K., Belanger, F., and Cuevas, L. (2006), “Potential of Environmental Models to Predict Meningitis Epidemics in Africa,” Tropical Medicine and International Health, 11 (6), 781–788. CrossRefGoogle Scholar
  31. Toni, T., Welch, D., Strelkowa, N., Ipsen, A., and Stumpf, M. (2009), “Approximate Bayesian Computation Scheme for Parameter Inference and Model Selection in Dynamical Systems,” Journal of the Royal Society Interface, 6 (31), 187. CrossRefGoogle Scholar
  32. Trotter, C., Gay, N., and Edmunds, W. (2005), “Dynamic Models of Meningococcal Carriage, Disease, and the Impact of Serogroup C Conjugate Vaccination,” American Journal of Epidemiology, 162 (1), 89. CrossRefGoogle Scholar
  33. Trotter, C., and Greenwood, B. (2007), “Meningococcal Carriage in the African Meningitis Belt,” Lancet. Infectious Diseases, 7 (12), 797–803. CrossRefGoogle Scholar

Copyright information

© International Biometric Society 2012

Authors and Affiliations

  1. 1.Department of StatisticsPennsylvania State UniversityUniversity ParkUSA
  2. 2.Department of Entomology and Center for Infectious Disease DynamicsPennsylvania State UniversityUniversity ParkUSA

Personalised recommendations