This paper develops two models for the dynamics of opinion change: an ODE model in which individual opinion is attracted by the opinions of major entities, such as government, professional organizations, and the broad community of contrarian influencers, and a advective-diffusive transport PDE model for the opinion density function. Examples probe the impact on opinion regarding vaccination resulting from changes in the expressed opinions of the governmental medical establishment.
This paper builds on Ledder (2022) by coupling epidemiological status (SIR) with vaccination attitude (Willing or Unwilling). The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.
Epidemiology models that incorporate vaccination generally assume that the entire susceptible population is in the queue to be vaccinated. COVID-19 showed us that this is a bad assumption. In this paper, I instead assume that a certain fraction of the population is willing to be vaccinated and divide the Susceptible class into Willing and Unwilling subgroups. Analysis on the endemic scale shows the impact that vaccine hesitancy can have on epidemiological scenarios. I also present a model on the epidemic time scale that accounts for issues involved in the vaccine rollout, where there can be limitations in both vaccine supply and vaccine administration capacity.
This paper examines a model in which two consumers compete for resources, with each of the consumers reproducing at discrete times while the resource reproduces continuously.
This paper develops a model of plant resource allocation between roots and shoots that is based on local control of resources, similar to what happens in obligate syntrophy. Local control produces results that are optimal in several senses.
We offer an innovative model for stem hydraulics that allows many of the properties of stems to be functions of path length from the base of the tree.
We offer an innovative model for stem hydraulics that allows many of the properties of stems to be functions of path length from the base of the tree.
Asymptotic methods are ubiquitous in models for physical science, but not often used in biological science. This is unfortunate, as many biological models have features that lend themselves to asymptotic methods. The first step in asymptotic analysis is scaling, which is not easy in biology. In this paper, I present some of the basic principles I use in scaling, using my onchocerciasis model as an example.
This paper presents a simple introduction to DEB models, using standard mathematical notation rather than the specialized system favored by most DEB practitioners, but somewhat unintelligible to the uninitiated.
This paper generalizes the Holling type II functional response model to more complicated settings.
This paper represents the "final word" on the spruce budworm model created by Ludwig, Jones, and Holling and previously analyzed by Brauer and Castillo-Chavez. Using asymptotic analysis, I identify various types of long-term behavior and link them to regions of the parameter space.
It is often assumed in DEB models that the death rate of organisms is simply a Poisson process; that is, that longevity is exponentially distributed. In this paper, we see that a consequence of this fact is that the optimal time for transitioning from growth to reproduction occurs when the population is still large; that is, it is optimal for a significant fraction of individuals to mature, but at a small size. This is not typical in nature, where most species have life histories in which a vanishingly small fraction of offspring survive to adulthood, where they have long careers in reproduction. The way to resolve this anomaly is to posit a hazard rate that is a sharply decreasing function of size rather than the constant implied by the exponential distribution.