
pmid: 40213022
pmc: PMC11982974
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.
17 pages, 7 figures
Physics - Physics and Society, Age-structured model, Populations and Evolution (q-bio.PE), [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Dynamical Systems (math.DS), Physics and Society (physics.soc-ph), Time since last infection, Partial differential equations, Article, Finite-size fluctuations, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, FOS: Biological sciences, [SDV.MHEP.MI] Life Sciences [q-bio]/Human health and pathology/Infectious diseases, FOS: Mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Dynamical Systems, Quantitative Biology - Populations and Evolution, Refractory density
Physics - Physics and Society, Age-structured model, Populations and Evolution (q-bio.PE), [MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS], FOS: Physical sciences, Dynamical Systems (math.DS), Physics and Society (physics.soc-ph), Time since last infection, Partial differential equations, Article, Finite-size fluctuations, [SDV.SPEE] Life Sciences [q-bio]/Santé publique et épidémiologie, FOS: Biological sciences, [SDV.MHEP.MI] Life Sciences [q-bio]/Human health and pathology/Infectious diseases, FOS: Mathematics, [MATH.MATH-AP] Mathematics [math]/Analysis of PDEs [math.AP], Mathematics - Dynamical Systems, Quantitative Biology - Populations and Evolution, Refractory density
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