Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination

Abstract

The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods.

Figure 1

Pneumococcal infection dynamics with vaccination as a function of age.

Figure 2

Reported and model calculated infections (left) and colonization prevalences (right) by age.

Figure 3

Model fit to 2 years of monthly case notifications (n₁ = 24). In the above legends, ‘data 1’ indicates the simulated data for age group 1, ‘model 1’ refers to the model solution for age group 1, ‘data 2’ is the plot of the data for age group 2, and so on. The model fit to 6 years (n₁ = 6) of simulated data is not shown.

Figure 4

Model with 5 age classes plotted with infection data grouped into 14 age classes. Again, in the legends above ‘data’ refers to the plotted simulated observations, ‘model’ indicates the corresponding model solutions, and the number indicates the age class.

Figure 5

Model with 5 age classes plotted with infection data grouped into 5 age classes.

Figure 6

Best fit model solutions to monthly case notifications with constant variance error.