Bayesian inference for infectious disease transmission models based on ordinary differential equations

Predicting the epidemiological effects of new vaccination
programmes through mathematical-statistical transmission modelling
is of increasing importance for the German Standing Committee on
Vaccination. Such models commonly capture large populations
utilizing a compartmental structure with its dynamics being
governed by a system of ordinary differential equations (ODEs).
Unfortunately, these ODE-based models are generally computationally
expensive to solve, which poses a challenge for any statistical
procedure inferring corresponding model parameters from disease
surveillance data. Thus, in practice parameters are often fixed
based on epidemiological knowledge hence ignoring uncertainty. A
Bayesian inference framework incorporating this prior knowledge
promises to be a more suitable approach allowing for additional
parameter flexibility. This thesis is concerned with statistical
methods for performing Bayesian inference of ODE-based models. A
posterior approximation approach based on a Gaussian distribution
around the posterior mode through its respective observed Fisher
information is presented. By employing a newly proposed method for
adjusting the likelihood impact in terms of using a power
posterior, the approximation procedure is able to account for the
residual autocorrelation in the data given the model. As an
alternative to this approximation approach, an adaptive
Metropolis-Hastings algorithm is described which is geared towards
an efficient posterior sampling in the case of a high-dimensional
parameter space and considerable parameter collinearities. In order
to identify relevant model components, Bayesian model selection
criteria based on the marginal likelihood of the data are applied.
The estimation of the marginal likelihood for each considered model
is performed via a newly proposed approach which utilizes the
available posterior sample obtained from the preceding
Metropolis-Hastings algorithm. Furthermore, the thesis contains an
application of the presented methods by predicting the
epidemiological effects of introducing rotavirus childhood
vaccination in Germany. Again, an ODE-based compartmental model
accounting for the most relevant transmission aspects of rotavirus
is presented. After extending the model with vaccination
mechanisms, it becomes possible to estimate the rotavirus vaccine
effectiveness through routinely collected surveillance data. By
employing the Bayesian framework, model predictions on the future
epidemiological development assuming a high vaccination coverage
rate incorporate uncertainty regarding both model structure and
parameters. The forecast suggests that routine vaccination may
cause a rotavirus incidence increase among older children and
elderly, but drastically reduces the disease burden among the
target group of young children, even beyond the expected direct
vaccination effect by means of herd protection. Altogether, this
thesis provides a statistical perspective on the modelling of
routine vaccination effects in order to assist decision making
under uncertainty. The presented methodology is thereby easily
applicable to other infectious diseases such as influenza.