arXiv subjects

Glenn Ledder

Publications and source records attributed to Glenn Ledder.

5 recordsLinked to original sources

arXiv2026

The Impact of Neglecting Vaccine Unwillingness in Epidemiology Models

With significant population fractions in many societies who refuse vaccines, it is important to reconsider how vaccination is incorporated into compartmental epidemiology models. It is still most common to apply the vaccination rate to the entire class of susceptibles, rather than to use the more realistic assumption that the vaccination rate function should depend only on the population of susceptibles who are willing and able to receive a vaccination. This study uses a simple generic disease model to address two questions: (1) How much error is introduced in key model outcomes by neglecting vaccine unwillingness?, and (2) Can the error be reduced by incorporating vaccine unwillingness into the vaccination rate constant rather than the rate diagram? The answers depend greatly on the time scale of interest. For the endemic time scale, where longterm behavior is studied with equilibrium point analysis, the error in neglecting unwillingess is large and cannot be improved upon by decreasing the vaccination rate constant. For the epidemic time scale, where the first big epidemic wave is studied with numerical simulations, the error can still be significant, particularly for diseases that are relatively less infectious and vaccination programs that are relatively slow.

q-bio.PE↗

arXiv2025

A Mathematical Model of Opinion Dynamics with Application to Vaccine Denial

Public health outcomes can be heavily influenced by the landscape of public opinion; hence, it is important to understand how that landscape changes over time. For one, opinions on public health issues are responsive to official pronouncements, whether from the governmental or professional medical establishments. Additionally, in today's world of high speed communication, opinion can also be highly responsive to the broadcast opinions of "influencers" whose large numbers of followers assure them of a broad reach. To understand the opinion landscape in a general sense, we develop an ordinary differential equation model for opinion change that is based primarily on attraction to the opinions of prominent sources. The individual opinion change model is then used to develop a Fokker-Planck-type partial differential equation model for the overall opinion landscape. This model is shown to have a stable equilibrium solution, and the dependence of the equilibrium solution on key model parameters is illustrated with examples based on opinion regarding vaccination.

physics.soc-ph↗

arXiv2024

Incorporating changeable attitudes toward vaccination into an SIR infectious disease model

We develop a mechanistic model that classifies individuals both in terms of epidemiological status (SIR) and vaccination attitude (willing or unwilling), with the goal of discovering how disease spread is influenced by changing opinions about vaccination. Analysis of the model identifies existence and stability criteria for both disease-free and endemic disease equilibria. The analytical results, supported by numerical simulations, show that attitude changes induced by disease prevalence can destabilize endemic disease equilibria, resulting in limit cycles.

math.DS↗

arXiv2023

Using asymptotics for efficient stability determination in epidemiological models

Analytical stability calculation is done to prove stability properties for systems with parameters that do not have explicit values. For systems with three components, the usual method of finding the characteristic polynomial as the determinant of J-lambda I and applying the Routh-Hurwitz conditions is reasonably efficient. For larger systems of four to six components, the method is impractical, as the calculations become too messy. In epidemiological models, there is often a very small parameter that appears as the ratio of a disease-based time scale to a demographic time scale; this allows efficient use of asymptotic approximation to simplify the calculations at little cost. Here we describe the tools and an example of efficient stability analysis, followed by a set of guidelines that are generally useful in applying the method.

math.DS↗

arXiv2017

A "Rule of Five" Framework for Models and Modeling to Unify Mathematicians and Biologists and Improve Student Learning

Despite widespread calls for the incorporation of mathematical modeling into the undergraduate biology curriculum, there is lack of a common understanding around the definition of modeling, which inhibits progress. In this paper, we extend the "Rule of Four," initially used in calculus reform efforts, to a framework for models and modeling that is inclusive of varying disciplinary definitions of each. This unifying framework allows us to both build on strengths that each discipline and its students bring, but also identify gaps in modeling activities practiced by each discipline. We also discuss benefits to student learning and interdisciplinary collaboration.

math.HO↗