Universal features of epidemic and vaccine models

TL;DR

This paper explores stochastic epidemic models with noise-induced transitions, analyzes the effects of vaccination and hesitancy, and reveals universal features shared with other dynamical systems, supported by COVID-19 data fitting.

Contribution

It introduces a stochastic SIS epidemic model with noise-induced bifurcations and a novel vaccine-hesitancy model with Beta-distributed steady states, linking epidemic dynamics to universal phenomena.

Findings

Bifurcation diagram shows unimodal and bimodal regimes with noise-induced transitions.

Vaccine hesitancy modeled with Beta distribution fits COVID-19 data well.

Steady-state distribution of the basic reproduction number derived from vaccination data.

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.