Stochastic Epidemic Models inference and diagnosis with Poisson Random Measure Data Augmentation

Exploring Zika's dynamics: A scoping review journey from epidemic to equations through mathematical modelling

Zika virus (ZIKV) infection, along with the concurrent circulation of other arboviruses, presents a great public health challenge, reminding the utilization of mathematical modelling as a crucial tool for explaining its intricate dynamics and interactions with co-circulating pathogens. Through a scoping review, we aimed to discern current mathematical models investigating ZIKV dynamics, focusing on its interplay with other pathogens, and to identify underlying assumptions and deficiencies supporting attention, particularly regarding the epidemiological attributes characterizing Zika outbreaks. Following the PRISMA-Sc guidelines, a systematic search across PubMed, Web of Science, and MathSciNet provided 137 pertinent studies from an initial pool of 2446 papers, showing a diversity of modelling approaches, predominantly centered on vector-host compartmental models, with a notable concentration on the epidemiological landscapes of Colombia and Brazil during the 2015-2016 Zika epidemic. While modelling studies have been important in explaining Zika transmission dynamics and their intersections with diseases such as Dengue, Chikungunya, and COVID-19 so far, future Zika models should prioritize robust data integration and rigorous validation against diverse datasets to improve the accuracy and reliability of epidemic prediction. In addition, models could benefit from adaptable frameworks incorporating human behavior, environmental factors, and stochastic parameters, with an emphasis on open-access tools to foster transparency and research collaboration.

A linear noise approximation for stochastic epidemic models fit to partially observed incidence counts

Stochastic epidemic models (SEMs) fit to incidence data are critical to elucidating outbreak dynamics, shaping response strategies, and preparing for future epidemics. SEMs typically represent counts of individuals in discrete infection states using Markov jump processes (MJPs), but are computationally challenging as imperfect surveillance, lack of subject-level information, and temporal coarseness of the data obscure the true epidemic. Analytic integration over the latent epidemic process is impossible, and integration via Markov chain Monte Carlo (MCMC) is cumbersome due to the dimensionality and discreteness of the latent state space. Simulation-based computational approaches can address the intractability of the MJP likelihood, but are numerically fragile and prohibitively expensive for complex models. A linear noise approximation (LNA) that approximates the MJP transition density with a Gaussian density has been explored for analyzing prevalence data in large-population settings, but requires modification for analyzing incidence counts without assuming that the data are normally distributed. We demonstrate how to reparameterize SEMs to appropriately analyze incidence data, and fold the LNA into a data augmentation MCMC framework that outperforms deterministic methods, statistically, and simulation-based methods, computationally. Our framework is computationally robust when the model dynamics are complex and applies to a broad class of SEMs. We evaluate our method in simulations that reflect Ebola, influenza, and SARS-CoV-2 dynamics, and apply our method to national surveillance counts from the 2013-2015 West Africa Ebola outbreak.