Inferring the effective reproductive number from deterministic and semi-deterministic compartmental models using incidence and mobility data.

The effective reproduction number (ℜt) is a theoretical indicator of the course of an infectious disease that allows policymakers to evaluate whether current or previous control efforts have been successful or whether additional interventions are necessary. This metric, however, cannot be directly observed and must be inferred from available data. One approach to obtaining such estimates is fitting compartmental models to incidence data. We can envision these dynamic models as the ensemble of structures that describe the disease's natural history and individuals' behavioural patterns. In the context of the response to the COVID-19 pandemic, the assumption of a constant transmission rate is rendered unrealistic, and it is critical to identify a mathematical formulation that accounts for changes in contact patterns. In this work, we leverage existing approaches to propose three complementary formulations that yield similar estimates for ℜt based on data from Ireland's first COVID-19 wave. We describe these Data Generating Processes (DGP) in terms of State-Space models. Two (DGP1 and DGP2) correspond to stochastic process models whose transmission rate is modelled as Brownian motion processes (Geometric and Cox-Ingersoll-Ross). These DGPs share a measurement model that accounts for incidence and transmission rates, where mobility data is assumed as a proxy of the transmission rate. We perform inference on these structures using Iterated Filtering and the Particle Filter. The final DGP (DGP3) is built from a pool of deterministic models that describe the transmission rate as information delays. We calibrate this pool of models to incidence reports using Hamiltonian Monte Carlo. By following this complementary approach, we assess the tradeoffs associated with each formulation and reflect on the benefits/risks of incorporating proxy data into the inference process. We anticipate this work will help evaluate the implications of choosing a particular formulation for the dynamics and observation of the time-varying transmission rate.

Anchoring the mean generation time in the SEIR to mitigate biases in ℜ0 estimates due to uncertainty in the distribution of the epidemiological delays.

The basic reproduction number, ℜ0, is of paramount importance in the study of infectious disease dynamics. Primarily, ℜ0 serves as an indicator of the transmission potential of an emerging infectious disease and the effort required to control the invading pathogen. However, its estimates from compartmental models are strongly conditioned by assumptions in the model structure, such as the distributions of the latent and infectious periods (epidemiological delays). To further complicate matters, models with dissimilar delay structures produce equivalent incidence dynamics. Following a simulation study, we reveal that the nature of such equivalency stems from a linear relationship between ℜ0 and the mean generation time, along with adjustments to other parameters in the model. Leveraging this knowledge, we propose and successfully test an alternative parametrization of the SEIR model that produces accurate ℜ0 estimates regardless of the distribution of the epidemiological delays, at the expense of biases in other quantities deemed of lesser importance. We further explore this approach's robustness by testing various transmissibility levels, generation times and data fidelity (overdispersion). Finally, we apply the proposed approach to data from the 1918 influenza pandemic. We anticipate that this work will mitigate biases in estimating ℜ0.

Shortcuts to adiabatic population inversion via time-rescaling: stability and thermodynamic cost.

A shortcut to adiabaticity is concerned with the fast and robust manipulation of the dynamics of a quantum system which reproduces the effect of an adiabatic process. In this work, we use the time-rescaling method to study the problem of speeding up the population inversion of a two-level quantum system, and the fidelity of the fast dynamics versus systematic errors in the control parameters. This approach enables the generation of shortcuts from a prescribed slow dynamics by simply rescaling the time variable of the quantum evolution operator. It requires no knowledge of the eigenvalues and eigenstates of the Hamiltonian and, in principle, no additional coupling fields. From a quantum thermodynamic viewpoint, we also demonstrate that the main properties of the distribution of work required to drive the system along the shortcuts are unchanged with respect to the reference (slow) protocol.

An evaluation of Hamiltonian Monte Carlo performance to calibrate age-structured compartmental SEIR models to incidence data.

Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo method to estimate unknown quantities through sample generation from a target distribution for which an analytical solution is difficult. The strength of this method lies in its geometrical foundations, which render it efficient for traversing high-dimensional spaces. First, this paper analyses the performance of HMC in calibrating five variants of inputs to an age-structured SEIR model. Four of these variants are related to restriction assumptions that modellers devise to handle high-dimensional parameter spaces. The other one corresponds to the unrestricted symmetric variant. To provide a robust analysis, we compare HMC's performance to that of the Nelder-Mead algorithm (NMS), a common method for non-linear optimisation. Furthermore, the calibration is performed on synthetic data in order to avoid confounding effects from errors in model selection. Then, we explore the variation in the method's performance due to changes in the scale of the problem. Finally, we fit an SEIR model to real data. In all the experiments, the results show that HMC approximates both the synthetic and real data accurately, and provides reliable estimates for the basic reproduction number and the age-dependent transmission rates. HMC's performance is robust in the presence of underreported incidences and high-dimensional complexity. This study suggests that stringent assumptions on age-dependent transmission rates can be lifted in favour of more realistic representations. The supplementary section presents the full set of results.