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We present a novel Exponential Time Differencing (ETD) scheme for nonlinear Riesz space fractional reaction-diffusion equations. This scheme is based on using a real distinct poles (RDP) discretization for the underlying matrix exponentials. Due to these RDP, the algorithm could be easily implemented in parallel to take advantage of multiple processors for increased computational efficiency. The method is established to be second-order convergent; and proven to be robust for problems involving non-smooth/mismatched initial and boundary conditions and steep solution gradients. We examine the stability of the scheme through its amplification factor and plot the boundaries of the stability regions comparative to other second-order ETD schemes. This numerical scheme combined with fractional central differencing is used for simulating some nonlinear space fractional problems. We demonstrate the superiority of our method over competing second-order ETD schemes, BDF2 scheme, and IMEX schemes. Our experiments show that the proposed scheme is computationally more efficient (in terms of cpu time). Furthermore, we investigate the trade-off between using fractional central differencing and matrix transfer technique in discretization of Riesz fractional derivatives. [ABSTRACT FROM AUTHOR]

Since early March 2020, government agencies have utilized a wide variety of non-pharmaceutical interventions to mitigate the spread of COVID-19 and have struggled to determine when it is appropriate to return to in-person activities after an outbreak is detected. At many universities, fundamental issues related to understanding the spread of the disease (e.g. the transmission rate), the ability of administrators to respond quickly enough by closing when there is a sudden rise in cases, and how to make a decision on when to reopen remains a concern. Surveillance testing strategies have been implemented in some places, and those test outcomes have dictated whether to reopen, to simultaneously monitor community spread, and/or to isolate discovered cases. However, the question remains as to when it is safe to reopen and how much testing is required to remain safely open while keeping infection numbers low. Here, we propose an extension of the classic SIR model to investigate reopening strategies for a fixed testing strategy, based on feedback from testing results. Specifically, we close when a predefined proportion of the population becomes infected, and later reopen when that infected proportion decreases below a predefined threshold. A valuable outcome of our approach is that our reopening strategies are robust to variation in almost all model parameters, including transmission rates, which can be extremely difficult to determine as they typically differ between variants, location, vaccination status, etc. Thus, these strategies can be, in theory, translated over to new variants in different regions of the world. Examples of robust feedback strategies for high disease transmission and a fixed testing capacity include (1) a single long lock down followed by a single long in-person period, and (2) multiple shorter lock downs followed by multiple shorter in-person periods. The utility of this approach of having multiple strategies is that administrators of universities, schools, business, etc. can use a strategy that is best adapted for their own functionality., Competing Interests: The authors have declared that no competing interests exist., (Copyright: © 2022 Dalton et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.)

Blebs, pressure driven protrusions of the cell membrane, facilitate the movement of eukaryotic cells such as the soil amoeba Dictyostelium discoideum, white blood cells and cancer cells. Blebs initiate when the cell membrane separates from the underlying cortex. A local rupture of the cortex, has been suggested as a mechanism by which blebs are initiated. However, much clarity is still needed about how cells inherently regulate rupture of the cortex in locations where blebs are expected to form. In this work, we examine the role of membrane energy and the motor protein myosin II (myosin) in facilitating the cell driven rupture of the cortex. We perform under-agarose chemotaxis experiments, using Dictyostelium discoideum cells, to visualize the dynamics of myosin and calculate changes in membrane energy in the blebbing region. To facilitate a rapid detection of blebs and analysis of the energy and myosin distribution at the cell front, we introduce an autonomous bleb detection algorithm that takes in discrete cell boundaries and returns the coordinate location of blebs with its shape characteristics. We are able to identify by microscopy naturally occurring gaps in the cortex prior to membrane detachment at sites of bleb nucleation. These gaps form at positions calculated to have high membrane energy, and are associated with areas of myosin enrichment. Myosin is also shown to accumulate in the cortex prior to bleb initiation and just before the complete disassembly of the cortex. Together our findings provide direct spatial and temporal evidence to support cortex rupture as an intrinsic bleb initiation mechanism and suggests that myosin clusters are associated with regions of high membrane energy where its contractile activity leads to a rupture of the cortex at points of maximal energy., Competing Interests: I have read the journal’s policy and the authors of this manuscript have the following competing interests. Author John Loustau was unable to confirm their authorship contributions. On their behalf, the corresponding author has reported their contributions to the best of their knowledge.