arXiv subjects

C. Franklin Goldsmith

Publications and source records attributed to C. Franklin Goldsmith.

3 recordsLinked to original sources

arXiv2020

Heterogeneity in susceptibility dictates the order of epidemiological models

The fundamental models of epidemiology describe the progression of an infectious disease through a population using compartmentalized differential equations, but do not incorporate population-level heterogeneity in infection susceptibility. We show that variation strongly influences the rate of infection, while the infection process simultaneously sculpts the susceptibility distribution. These joint dynamics influence the force of infection and are, in turn, influenced by the shape of the initial variability. Intriguingly, we find that certain susceptibility distributions (the exponential and the gamma) are unchanged through the course of the outbreak, and lead naturally to power-law behavior in the force of infection; other distributions often tend towards these "eigen-distributions" through the process of contagion. The power-law behavior fundamentally alters predictions of the long-term infection rate, and suggests that first-order epidemic models that are parameterized in the exponential-like phase may systematically and significantly over-estimate the final severity of the outbreak.

q-bio.PE↗

arXiv2020

Population Susceptibility Variation and Its Effect on Contagion Dynamics

Susceptibility governs the dynamics of contagion. The classical SIR model is one of the simplest compartmental models of contagion spread, assuming a single shared susceptibility level. However, variation in susceptibility over a population can fundamentally affect the dynamics of contagion and thus the ultimate outcome of a pandemic. We develop mathematical machinery which explicitly considers susceptibility variation, illuminates how the susceptibility distribution is sculpted by contagion, and thence how such variation affects the SIR differential questions that govern contagion. Our methods allow us to derive closed form expressions for herd immunity thresholds as a function of initial susceptibility distributions and suggests an intuitively satisfying approach to inoculation when only a fraction of the population is accessible to such intervention. Of particular interest, if we assume static susceptibility of individuals in the susceptible pool, ignoring susceptibility diversity {\em always} results in overestimation of the herd immunity threshold and that difference can be dramatic. Therefore, we should develop robust measures of susceptibility variation as part of public health strategies for handling pandemics.

q-bio.PE↗

arXiv2017

The Impact of Roaming Radicals on the Combustion Properties of Transportation Fuels

A systematic investigation on the effects of roaming radical reactions on global combustion properties for transportation fuels is presented. New software was developed that can automatically discover all the possible roaming pathways within a given chemical kinetic mechanism. This novel approach was applied to two mechanisms taken from the literature, one for heptane and one for butanol. Ignition delay times and laminar flame speeds were computed over a broad range of conditions, while testing varying degrees of roaming. As the degree of roaming is increased, the ignition delays increased, consistent with the hypothesis that roaming decreases the reactivity of the system. The percent increase in the ignition delay is strongly temperature dependent, with the largest effect seen in the negative temperature coefficient regime. Outside of this temperature range, the effect of roaming on global combustion properties is small, on the order of a few percent for ignition delays and less than a percent for flame speeds. The software that was used to create the new mechanisms and test the effects of roaming on combustion properties are freely available, with detailed tutorials that will enable it to be applied to fuels other than heptane and butanol.

physics.chem-ph↗