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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2507.01310 |
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| _version_ | 1866909672006483968 |
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| author | Chowdhury, Sourav Bose, Indrani Roychowdhury, Suparna Chaudhuri, Indranath |
| author_facet | Chowdhury, Sourav Bose, Indrani Roychowdhury, Suparna Chaudhuri, Indranath |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01310 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal features of epidemic and vaccine models Chowdhury, Sourav Bose, Indrani Roychowdhury, Suparna Chaudhuri, Indranath Populations and Evolution Biological Physics 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. |
| title | Universal features of epidemic and vaccine models |
| topic | Populations and Evolution Biological Physics |
| url | https://arxiv.org/abs/2507.01310 |