ArticleScientific reports2019
Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations.
Article in Scientific reports, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 10 papers.
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10 citing papers in PubMed.
- How immunity shapes the long-term dynamics of influenza H3N2.PLoS computational biology · 2025Article
- Quantum-Like Approaches Unveil the Intrinsic Limits of Predictability in Compartmental Models.Entropy (Basel, Switzerland) · 2024Article
- Uncertainty analysis of contagion processes based on a functional approach.Scientific reports · 2023Article
- Infectious Disease Modeling with Socio-Viral Behavioral Aspects-Lessons Learned from the Spread of SARS-CoV-2 in a University.Tropical medicine and infectious disease · 2022Article
- Strain-stream model of epidemic spread in application to COVID-19.The European physical journal. B · 2022Article
- Response: Commentary: Statistical Modeling for the Prediction of Infectious Disease Dissemination With Special Reference to COVID-19 Spread.Frontiers in public health · 2021Article
- Estimation of the probability of daily fluctuations of incidence of COVID-19 according to official data.PeerJ · 2021Article
- Viral disease spreading in grouped population.Computer methods and programs in biomedicine · 2020Article
- COVID-19 in India: Statewise Analysis and Prediction.JMIR public health and surveillance · 2020Article
- Mathematical Modelling to Assess the Impact of Lockdown on COVID-19 Transmission in India: Model Development and Validation.JMIR public health and surveillance · 2020Article
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2 authors.
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Abstract
Empirical records of epidemics reveal that fluctuations are important factors for the spread and prevalence of infectious diseases. The exact manner in which fluctuations affect spreading dynamics remains poorly known. Recent analytical and numerical studies have demonstrated that improved differential equations for mean and variance of infected individuals reproduce certain regimes of the SIS epidemic model. Here, we show they form a dynamical system that follows Hamilton's equations, which allow us to understand the role of fluctuations and their effects on epidemics. Our findings show the Hamiltonian is a constant of motion for large population sizes. For small populations, finite size effects break the temporal symmetry and induce a power-law decay of the Hamiltonian near the outbreak onset, with a parameter-free exponent. Away from the onset, the Hamiltonian decays exponentially according to a constant relaxation time, which we propose as a metric when fluctuations cannot be neglected.
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