arXiv subjects

Joseph Hickey

Publications and source records attributed to Joseph Hickey.

3 recordsLinked to original sources

arXiv2024

Do the unvaccinated disproportionately harm the vaccinated in a respiratory pandemic?

A parameter $\psi$ was recently defined and introduced into the epidemiological modelling scientific literature, and is being accepted. The said parameter was used to argue that there was a disproportionate risk of infection incurred by vaccinated persons due to contacts with unvaccinated persons during the declared COVID-19 pandemic. Opposing published results show that, in general, there is virtually never a disproportionate risk to the vaccinated from the unvaccinated during a respiratory pandemic. Here, we show that the newly introduced vaccinology parameter $\psi$ is incorrectly defined and that the conclusions of disproportionate risk are not valid. Specifically, we prove that the originating authors Fisman et al. (2022, 2024) incorrectly defined and applied the parameter $\psi$. Their application would imply that the said risk increases with increasing segregation from the unvaccinated (up to complete segregation), increases with increasing vaccination coverage (up to complete coverage) and increases with increasing vaccine efficacy (up to perfect vaccine efficacy), which is impossible. Use of the erroneous parameter $\psi$ has the potential to encourage unnecessarily aggressive public health policies and interventions.

physics.soc-ph↗

arXiv2023

Simple model of market share dynamics based on clients' firm-switching decisions

Firms compete for clients, creating distributions of market shares ranging from domination by a few giant companies to markets in which there are many small firms. These market structures evolve in time, and may remain stable for many years before a new firm emerges and rapidly obtains a large market share. We seek the simplest realistic model giving rise to such diverse market structures and dynamics. We focus on markets in which every client adopts a single firm, and can, from time to time, switch to a different firm. Examples include markets of cell phone and Internet service providers, and of consumer products with strong brand identification. In the model, the size of a particular firm, labelled $i$, is equal to its current number of clients, $n_i$. In every step of the simulation, a client is chosen at random, and then selects a firm from among the full set of firms with probability $p_i = (n_i^α+ β)/K$, where $K$ is the normalization factor. Our model thus has two parameters: $α$ represents the degree to which firm size is an advantage ($α$ > 1) or disadvantage ($α$ < 1), relative to strict proportionality to size ($α$ = 1), and $β$ represents the degree to which small firms are viable despite their small size. We postulate that $α$ and $β$ are determined by the regulatory, technology, business culture and social environments. The model exhibits a phase diagram in the parameter space, with different regions of behaviour. At the large $α$ extreme of the phase diagram, a single dominant firm emerges, whose market share depends on the value of $β$. At the small $α$ extreme, many firms with small market shares coexist, and no dominant firm emerges. In the intermediate region, markets are divided among a relatively small number of firms, each with sizeable market share but with distinct rankings, which can persist for long [...]

physics.soc-ph↗

arXiv2018

Self-organization and time-stability of social hierarchies

The formation and stability of social hierarchies is a question of general relevance. Here, we propose a simple generalized theoretical model for establishing social hierarchy via pair-wise interactions between individuals and investigate its stability. In each interaction or fight, the probability of "winning" depends solely on the relative societal status of the participants, and the winner has a gain of status whereas there is an equal loss to the loser. The interactions are characterized by two parameters. The first parameter represents how much can be lost, and the second parameter represents the degree to which even a small difference of status can guarantee a win for the higher-status individual. Depending on the parameters, the resulting status distributions reach either a continuous unimodal form or lead to a totalitarian end state with one high-status individual and all other individuals having status approaching zero. However, we find that in the latter case long-lived intermediary distributions often exist, which can give the illusion of a stable society. As we show, our model allows us to make predictions consistent with animal interaction data and their evolution over a number of years. Moreover, by implementing a simple, but realistic rule that restricts interactions to sufficiently similar-status individuals, the stable or long-lived distributions acquire high-status structure corresponding to a distinct high-status class. Using household income as a proxy for societal status in human societies, we find agreement over their entire range from the low-to-middle-status parts to the characteristic high-status "tail". We discuss how the model provides a conceptual framework for understanding the origin of social hierarchy and the factors which lead to the preservation or deterioration of the societal structure.

physics.soc-ph↗