paper

Universal features of epidemic and vaccine models

arXiv:2507.01310 · doi:10.1103/11qy-2gc3

Abstract

In this paper, we study a stochastic susceptible-infected-susceptible (SIS) epidemic model that includes an additional immigration process. In the presence of multiplicative noise, generated by environmental perturbations, the model exhibits noise-induced transitions. The bifurcation diagram has two distinct regions of unimodality and bimodality in which the steady-state probability distribution has one and two peaks, respectively. Apart from first-order transitions between the two regimes, a critical-point transition occurs at a cusp point with the transition belonging to the mean-field Ising universality class. The epidemic model shares these features with the well-known Horsthemke-Lefever model of population genetics. The effect of vaccination on the spread/containment of the epidemic in a stochastic setting is also studied. We further propose a general vaccine-hesitancy model, along the lines of Kirman's ant model, with the steady-state distribution of the fraction of the vaccine-willing population given by the Beta distribution. The distribution is shown to give a good fit to the COVID-19 data on vaccine hesitancy and vaccination. We derive the steady-state probability distribution of the basic reproduction number, a key parameter in epidemiology, based on a beta-distributed fraction of the vaccinated population. Our study highlights the universal features that epidemic and vaccine models share with other dynamical models.

14 pages, 12 captioned figures

References in corpus (8)