The 2019 Novel Corona virus infection (COVID 19) is an ongoing public health emergency of international focus. Significant gaps persist in our knowledge of COVID 19 epidemiology, transmission dynamics, investigation tools and management, despite (or possibly because of) the fact that the outbreak is an unprecedented global threat. On the positive side, enough is currently known about the epidemic process to permit the construction of mathematical predictive models. In our work, we adapt a traditional SEIR epidemic model to the specific dynamic compartments and epidemic parameters of COVID 19, as it spreads in an age-heterogeneous community. We analyze management strategies of the epidemic course (as they were implemented through lockdown and reopening procedures in many of the US states and countries worldwide); however, to more clearly illustrate ideas, we focus on the example of a small scale college town community, with the timeline of control measures introduced in the state of New York. We generate predictions, and assess the efficiency of these control measures (closures, mobility restrictions, social distancing), in a sustainability context.

Lead is a naturally-occurring element. It has been known to man for a long time, and it is one of the longest established poisons. The current consensus is that no level of lead exposure should be deemed “safe”. New evidence regarding the blood levels at which morbidities occur has prompted the CDC to reduce the screening guideline of 10 μg/dl to 2 μg/dl. Measurable cognitive decline (reduced IQ, academic deficits) have been found to occur at levels below 10 μg/dl, especially in children. Knowledge of lead pharmacology allows us to better understand its absorption and metabolization, mechanisms that produce its medical consequences. Based upon an original and very simplified compartmental model of Rabinowitz (1973) with only three major compartments (blood, bone and soft tissue), extensive biophysical models sprouted over the following two decades. However, none of these models have been specifically designed to use new knowledge of lead molecular dynamics to understand its deleterious effects on the brain. We build and analyze a compartmental model of lead pharmacokinetics, focused specifically on addressing neurotoxicity. We use traditional phase space methods, parameter sensitivity analysis and bifurcation theory to study the transitions in the system’s behavior in response to various physiological parameters. We conclude that modeling the complex interaction of lead and calcium along their dynamic trajectory may successfully explain counter-intuitive effects on systemic function and neural behavior which could not be addressed by existing linear models. Our results encourage further efforts towards using nonlinear phenomenology in conjunction with empirically driven system parameters, to obtain a biophysical model able to provide clinical assessments and predictions.

It has previously been established that, in threatening situations, animals use alarm pheromones to communicate danger. There is emerging evidence of analogous chemosensory “stress” cues in humans. For this study, we collected alarm and exercise sweat from “donors,” extracted it, pooled it and presented it to 16 unrelated “detector” subjects undergoing fMRI. The fMRI protocol consisted of four stimulus runs, with each combination of stimulus condition and donor gender represented four times. Because olfactory stimuli do not follow the canonical hemodynamic response, we used a model-free approach. We performed minimal preprocessing and worked directly with block-average time series and step-function estimates. We found that, while male stress sweat produced a comparably strong emotional response in both detector genders, female stress sweat produced a markedly stronger arousal in female than in male detectors. Our statistical tests pinpointed this gender-specificity to the right amygdala (strongest in the superficial nuclei). When comparing the olfactory bulb responses to the corresponding stimuli, we found no significant differences between male and female detectors. These imaging results complement existing behavioral evidence, by identifying whether gender differences in response to alarm chemosignals are initiated at the perceptual versus emotional level. Since we found no significant differences in the olfactory bulb (primary processing site for chemosensory signals in mammals), we infer that the specificity in responding to female fear is likely based on processing meaning, rather than strength, of chemosensory cues from each gender.

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