Periodicity, synchronization and persistence in pre-vaccination measles

Marguta, Ramona; Parisi, Andrea

doi:10.1098/rsif.2016.0258

Cited by 5 publications

(9 citation statements)

References 23 publications

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“…Our findings are similar in many aspects to the ones obtained for the case of measles and, more in general, for a SIR model with vital dynamics and external introductions [27,49,28,30,31,23,24,47,50,51]. This exemplifies that different mechanisms of susceptible replenishment can lead to common dynamical features.…”

Section: Resultssupporting

confidence: 87%

Human mobility networks and persistence of rapidly mutating pathogens

et al. 2017

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Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts’ acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts’ mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts’ mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.

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Section: Resultssupporting

confidence: 87%

Human mobility networks and persistence of rapidly mutating pathogens

et al. 2017

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“…Experiments on the effects of migration between metapopulations, i.e. similar populations but spatially separated, subjected to temporal fluctuations have shown that pathogen prevalence is greatly influenced by the nature of the fluctuation 23 , highlighting the interplay between synchronization and pathogen prevalence in epidemics 24 .…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

Nakamura¹,

Martinêz²

2019

Sci Rep

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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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“…We estimate the movement of individuals within each country using the Radiation Model [24, 25] fitted on commuting data. Individual have a set of preferred locations, with an associated frequency of visit, which is assigned at the start of the simulation based on the fluxes between grid elements estimated by the radiation model [26, 27]. Each day a destination is chosen for each individual among his set of preferred locations according to their frequency of visit, and the individual is moved to that preferred location where it participates to the dynamics of that cell for a duration corresponding to the average work day.…”

Section: Methodsmentioning

confidence: 99%

“…Our simulation model uses grid elements as basic areal units, thus we identified the grid cells corresponding to the different national subdivisions specified by the commuting matrices, and calculated the corresponding aggregated fluxes. These fluxes depend on the fraction of the population participating in the global commuting between regions which is a model parameter [26, 27]: the optimal value was identified by maximizing the common part of commuters – a measure of similarity of flow estimates based on the Sørensen index [29, 30, 31]. Further details are available in the Supplementary Material SM-1.…”

Section: Methodsmentioning

confidence: 99%

Spatially resolved simulations of the spread of COVID-19 in European countries

Parisi

Brand

Hilton

et al. 2020

Preprint

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We explore the spatial and temporal spread of the novel SARS-CoV-2 virus under containment measures in three European countries based on fits to data of the early outbreak. Using data from Spain and Italy, we estimate an age dependent infection fatality ratio for SARS-CoV-2, as well as risks of hospitalization and intensive care admission. We use them in a model that simulates the dynamics of the virus using an age structured, spatially detailed agent based approach, that explicitly incorporates governamental interventions, changes in mobility and contact patterns occurred during the COVID-19 outbreak in each country. Our simulations reproduce several of the features of its spatio-temporal spread in the three countries studied. They show that containment measures combined with high density are responsible for the containment of cases within densely populated areas, and that spread to less densely populated areas occurred during the late stages of the first wave. The capability to reproduce observed features of the spatio-temporal dynamics of SARS-CoV-2 makes this model a potential candidate for forecasting the dynamics of SARS-CoV-2 in other settings, and we recommend its application in low and lower-middle countries which remain understudied.

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Periodicity, synchronization and persistence in pre-vaccination measles

Cited by 5 publications

References 23 publications

Human mobility networks and persistence of rapidly mutating pathogens

Human mobility networks and persistence of rapidly mutating pathogens

Hamiltonian dynamics of the SIS epidemic model with stochastic fluctuations

Spatially resolved simulations of the spread of COVID-19 in European countries

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