Balancing mitigation strategies for viral outbreaks.

Control and prevention strategies are indispensable tools for managing the spread of infectious diseases. This paper examined biological models for the post-vaccination stage of a viral outbreak that integrate two important mitigation tools: social distancing, aimed at reducing the disease transmission rate, and vaccination, which boosts the immune system. Five different scenarios of epidemic progression were considered: (ⅰ) the "no control" scenario, reflecting the natural evolution of a disease without any safety measures in place, (ⅱ) the "reconstructed" scenario, representing real-world data and interventions, (ⅲ) the "social distancing control" scenario covering a broad set of behavioral changes, (ⅳ) the "vaccine control" scenario demonstrating the impact of vaccination on epidemic spread, and (ⅴ) the "both controls concurrently" scenario incorporating social distancing and vaccine controls simultaneously.

Polyglot entrainment for higher dimensional neuronal models.

The entrainment of biological oscillators is a classic problem in the field of dynamical systems and synchronization. This paper explores a novel type of entrainment mechanism referred to as polyglot entrainment [Khan et al., "The emergence of polyglot entrainment responses to periodic inputs in vicinities of Hopf bifurcations in slow-fast systems," Chaos 32, 063137 (2022)] (multiple disconnected 1:1 regions for a range of forcing amplitude) for higher dimensional nonlinear systems.

A Simplified Mathematical Model for Cell Proliferation in a Tissue-Engineering Scaffold.

While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior-particularly nutrient consumption and depletion within the scaffold-has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. This work presents a comprehensive continuum model for cell proliferation within two-dimensional tissue-engineering scaffolds.

Effects of Elasticity on Cell Proliferation in a Tissue-Engineering Scaffold Pore.

Scaffolds engineered for in vitro tissue engineering consist of multiple pores where cells can migrate along with nutrient-rich culture medium. The presence of the nutrient medium throughout the scaffold pores promotes cell proliferation, and this process depends on several factors such as scaffold geometry, nutrient medium flow rate, shear stress, cell-scaffold focal adhesions and elastic properties of the scaffold material. While numerous studies have addressed the first four factors, the mathematical approach described herein focuses on cell proliferation rate in elastic scaffolds, under constant flux of nutrients.

Curvature- and fluid-stress-driven tissue growth in a tissue-engineering scaffold pore.

Cell proliferation within a fluid-filled porous tissue-engineering scaffold depends on a sensitive choice of pore geometry and flow rates: regions of high curvature encourage cell proliferation, while a critical flow rate is required to promote growth for certain cell types. When the flow rate is too slow, the nutrient supply is limited; when it is too fast, cells may be damaged by the high fluid shear stress. As a result, determining appropriate tissue-engineering-construct geometries and operating regimes poses a significant challenge that cannot be addressed by experimentation alone.