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

ABSTRACT: 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.

SUBMITTER: Andrade J

PROVIDER: S-EPMC9269962 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:BackgroundWhen assessing connectivity, it is crucial to rely on accurate modeling frameworks that consider species movement preferences and patterns. One important aspect is the level of randomness or unpredictability in the route selection. In this respect, traditional approaches (based on least-cost path or circuit theory) consider species movements unrealistically as totally deterministic or as totally random. A recent approach (randomized shortest path) advocates for choosing intermediate levels of randomness through a single parameter. This parameter may be optimized by validating connectivity surfaces developed from different levels of randomness against observed movement data. However, connectivity models are seldom validated, and it is still unclear how to approach this task. To address this knowledge gap, this paper aims at comparing different validation methods to infer the optimal randomness level in connectivity studies. Additionally, we aimed to disentangle the practical consequences of applying traditional connectivity approaches versus using an optimized level of movement randomness when delineating corridors.MethodsThese objectives were accomplished through the study case of the Iberian lynx, an endangered species whose maintenance and recovery depend on the current connectivity among its population nuclei. We firstly determined a conductance surface based on point selection functions accounting for the behavioral state (territorial or exploratory) of individuals. Secondly, we identified the level of randomness that better fits lynxes' movements with independent GPS locations and different validation techniques. Lastly, we delineated corridors between lynx population nuclei through a) the randomized shortest path approach and the extreme and optimal levels of randomness of each validation method, and b) the traditional connectivity approaches.ResultsAccording to all used validation methodologies, models with intermediate levels of randomness outperformed those with extreme randomness levels representing totally deterministic or random movements. We found differences in the optimal randomness level among validation methods but similar results in the delineation of corridors. Our results also revealed that models with extreme randomness levels (deterministic and random walk) of the randomized path approach provided equivalent corridor networks to those from traditional approaches. Moreover, these corridor networks calculated with traditional approaches showed notable differences in patterns from the corridor network calculated with an optimized randomness level.ConclusionsHere we presented a connectivity model with a solid biological basis that calibrates the level of movement randomness and is supported by comprehensive validation methods. It is thus a step forward in the search and evaluation of connectivity approaches that lead to improved, efficient, and successful management actions.

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

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