Modelling dynamics between free-living amoebae and bacteria.

Free-living amoebae (FLA) serve as hosts for a variety of endosymbionts, which are microorganisms that reside and multiply within the FLA. Some of these endosymbionts pose a pathogenic threat to humans, animals, or both. The symbiotic relationship with FLA not only offers these microorganisms protection but also enhances their survival outside their hosts and assists in their dispersal across diverse habitats, thereby escalating disease transmission. This review is intended to offer an exhaustive overview of the existing mathematical models that have been applied to understand the dynamics of FLA, especially concerning their interactions with bacteria. An extensive literature review was conducted across Google Scholar, PubMed, and Scopus databases to identify mathematical models that describe the dynamics of interactions between FLA and bacteria, as published in peer-reviewed scientific journals. The literature search revealed several FLA-bacteria model systems, including Pseudomonas aeruginosa, Pasteurella multocida, and Legionella spp. Although the published mathematical models account for significant system dynamics such as predator-prey relationships and non-linear growth rates, they generally overlook spatial and temporal heterogeneity in environmental conditions, such as temperature, and population diversity. Future mathematical models will need to incorporate these factors to enhance our understanding of FLA-bacteria dynamics and to provide valuable insights for future risk assessment and disease control measures.

Capturing the Effects of Transportation on the Spread of COVID-19 With a Multi-Networked SEIR Model.

In this letter we present a deterministic discrete-time networked SEIR model that includes a number of transportation networks, and present assumptions under which it is well defined. We analyze the limiting behavior of the model and present necessary and sufficient conditions for estimating the spreading parameters from data. We illustrate these results via simulation and with real COVID-19 data from the Northeast United States, integrating transportation data into the results.