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

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.