A refractory density approach to a multi-scale SEIRS epidemic model

TL;DR

This paper introduces a multi-scale epidemic model based on the Refractory Density approach, capturing complex disease dynamics across individual, population, and macro scales with stochastic effects.

Contribution

It presents a novel multi-scale modeling framework for infectious diseases that integrates microscopic, mesoscopic, and macroscopic descriptions using the RD approach.

Findings

The model captures transient and asymptotic epidemic dynamics.

It accounts for finite-size fluctuations and stochastic effects.

Comparison with coronavirus data supports the model's relevance.

Abstract

We propose a novel multi-scale modeling framework for infectious disease spreading, borrowing ideas and modeling tools from the so-called Refractory Density (RD) approach. We introduce a microscopic model that describes the probability of infection for a single individual and the evolution of the disease within their body. From the individual-level description, we then present the corresponding population-level model of epidemic spreading on the mesoscopic and macroscopic scale. We conclude with numerical illustrations taking into account either a white Gaussian noise or an escape noise to showcase the potential of our approach in producing both transient and asymptotic complex dynamics as well as finite-size fluctuations consistently across multiple scales. A comparison with the epidemiology of coronaviruses is also given to corroborate the qualitative relevance of our new approach.