Mathematical model for rod outer segment dynamics during retinal detachment.

Retinal detachment (RD) is the separation of the neural layer from the retinal pigmented epithelium thereby preventing the supply of nutrients to the cells within the neural layer of the retina. In vertebrates, primary photoreceptor cells consisting of rods and cones undergo daily renewal of their outer segment through the addition of disc-like structures and shedding of these discs at their distal end. When the retina detaches, the outer segment of these cells begins to degenerate and, if surgical procedures for reattachment are not done promptly, the cells can die and lead to blindness. The precise effect of RD on the renewal process is not well understood. Additionally, a time frame within which reattachment of the retina can restore proper photoreceptor cell function is not known. Focusing on rod cells, we propose a mathematical model to clarify the influence of retinal detachment on the renewal process. Our model simulation and analysis suggest that RD stops or significantly reduces the formation of new discs and that an alternative removal mechanism is needed to explain the observed degeneration during RD. Sensitivity analysis of our model parameters points to the disc removal rate as the key regulator of the critical time within which retinal reattachment can restore proper photoreceptor cell function.

Modeling optimal reopening strategies for COVID-19 and its variants by keeping infections low and fixing testing capacity.

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.