Modeling and inference for infectious disease dynamics: a likelihood-based approach - PubMed (original) (raw)

Modeling and inference for infectious disease dynamics: a likelihood-based approach

Carles Bretó. Stat Sci. 2018 Feb.

Abstract

Likelihood-based statistical inference has been considered in most scientific fields involving stochastic modeling. This includes infectious disease dynamics, where scientific understanding can help capture biological processes in so-called mechanistic models and their likelihood functions. However, when the likelihood of such mechanistic models lacks a closed-form expression, computational burdens are substantial. In this context, algorithmic advances have facilitated likelihood maximization, promoting the study of novel data-motivated mechanistic models over the last decade. Reviewing these models is the focus of this paper. In particular, we highlight statistical aspects of these models like overdispersion, which is key in the interface between nonlinear infectious disease modeling and data analysis. We also point out potential directions for further model exploration.

Keywords: Lévy-driven stochastic differential equation; compartment model; continuous-time Markov chain; environmental stochasticity; iterated filtering; maximum likelihood; particle filter.

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Figures

Fig 1

Fig 1

Example of diagrammatic representation of a mechanistic partially observed Markov process model of the susceptible-infectious-removed-susceptible type. Observed data and demography are also represented. The three boxes highlight a biological disease transmission mechanism where flows can occur at different rates (represented by arrow labels) between three stages (or compartments): susceptible, infectious and removed (or recovered). To deal with demography (i.e., biological births and deaths), a set of flows to and from a fictitious fourth demographic stage is also included. Due to partial observation, all data y1:N∗ come from the infectious stage only and at times t1, …, tN only (see Section 2 for details on notation).

Fig 2

Fig 2

Iterated filtering algorithms rely on extending a partially observed Markov process model of interest by introducing random perturbations to the model parameters θ to then explore the original space of θ searching for values that are more likely to have produced the observed data. Convergence to a maximum likelihood estimate has been established for appropriately constructed procedures that iterate this search over the parameter space while diminishing the intensity of perturbations (Ionides, Bretó and King, 2006; Ionides et al., 2011, 2015). The role and timeliness of iterated filtering algorithms for infectious disease modeling have recently been pointed out (Dobson, 2014).

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