Edge-based compartmental modelling for infectious disease spread

Miller, Joel C.; Slim, Anja C.; Volz, Erik

doi:10.1098/rsif.2011.0403

Cited by 232 publications

(307 citation statements)

References 50 publications

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“…The specific limits may typically depend on the size and type of the network or the time horizon over which agreement is sought. The main candidate models include the pairwise [8], edge-based compartmental models [12], as well as effective-degree type models [10,11] which have mainly originated from epidemic models such as the SIS and SIR (S -susceptible, I -infected and infectious and R -recovered or removed). For all these models, the primary test of their performance, is in terms of the agreement between the time evolution of some expected quantity (e.g.…”

Section: Introductionmentioning

confidence: 99%

Approximate Master Equations for Dynamical Processes on Graphs

Nagy

Kiss

Šimon

2014

Math. Model. Nat. Phenom.

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Abstract. We extrapolate from the exact master equations of epidemic dynamics on fully connected graphs to non-fully connected by keeping the size of the state space N + 1, where N is the number of nodes in the graph. This gives rise to a system of approximate ODEs (ordinary differential equations) where the challenge is to compute/approximate analytically the transmission rates. We show that this is possible for graphs with arbitrary degree distributions built according to the configuration model. Numerical tests confirm that: (a) the agreement of the approximate ODEs system with simulation is excellent and (b) that the approach remains valid for clustered graphs with the analytical calculations of the transmission rates still pending. The marked reduction in state space gives good results, and where the transmission rates can be analytically approximated, the model provides a strong alternative approximate model that agrees well with simulation. Given that the transmission rates encompass information both about the dynamics and graph properties, the specific shape of the curve, defined by the transmission rate versus the number of infected nodes, can provide a new and different measure of network structure, and the model could serve as a link between inferring network structure from prevalence or incidence data.

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Section: Introductionmentioning

confidence: 99%

Approximate Master Equations for Dynamical Processes on Graphs

Nagy

Kiss

Šimon

2014

Math. Model. Nat. Phenom.

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“…Because the final size Z is a decelerating function of the reproduction number R (figure 1a), antipyresis always enhances transmission more for less transmissible diseases (which have smaller R 0 : figure 1b). The precise quantitative predictions in figure 1b depend on our use of the standard final size relation; however, the qualitative conclusions are very general because the expected final size always increases (typically in a decelerating fashion) as R increases [27][28][29][30][31].…”

Section: Theoretical Argumentmentioning

confidence: 99%

Population-level effects of suppressing fever

Earn

Andrews

2014

Proc. R. Soc. B.

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Fever is commonly attenuated with antipyretic medication as a means to treat unpleasant symptoms of infectious diseases. We highlight a potentially important negative effect of fever suppression that becomes evident at the population level: reducing fever may increase transmission of associated infections. A higher transmission rate implies that a larger proportion of the population will be infected, so widespread antipyretic drug use is likely to lead to more illness and death than would be expected in a population that was not exposed to antipyretic pharmacotherapies. We assembled the published data available for estimating the magnitudes of these individual effects for seasonal influenza. While the data are incomplete and heterogeneous, they suggest that, overall, fever suppression increases the expected number of influenza cases and deaths in the US: for pandemic influenza with reproduction number R 1:8, the estimated increase is 1% (95% CI: 0.0-2.7%), whereas for seasonal influenza with R 1:2, the estimated increase is 5% (95% CI: 0.2-12.1%).

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“…For a more detailed derivation of the analogous results for the special case of a single type network, see [13,14].…”

Section: Volz-miller Mean-field Sir In Multitype Networkmentioning

confidence: 99%

“…However for our purposes, it will be sufficient to focus on the behavior of extensive outbreaks (i.e., those which scale with the system size), the average dynamics of which, can be derived in the limit when the number of nodes tends to infinity, by generalizing a mean-field technique for single type networks, developed by Volz and Miller, to multitype networks. Below, we follow the basic structure of the derivations presented in [13,14].…”

Section: Volz-miller Mean-field Sir In Multitype Networkmentioning

confidence: 99%

Epidemic fronts in complex networks with metapopulation structure

et al. 2013

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Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and "patchy" organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure. We first present a generalization of the Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR) dynamics on multitype networks. We then use this technique to study the special case of epidemic fronts propagating on a one-dimensional lattice of interconnected networks -representing a simple chain of coupled population centers -as a necessary first step in understanding how macro-scale disease spread depends on micro-scale topology. Using the formalism of front propagation into unstable states, we derive the effective transport coefficients of the linear spreading: asymptotic speed, characteristic wavelength, and diffusion coefficient for the leading edge of the pulled fronts, and analyze their dependence on the underlying graph structure. We also derive the epidemic threshold for the system and study the front profile for various network configurations. To our knowledge, this is the first such application of front propagation concepts to random network models.

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Edge-based compartmental modelling for infectious disease spread

Cited by 232 publications

References 50 publications

Approximate Master Equations for Dynamical Processes on Graphs

Approximate Master Equations for Dynamical Processes on Graphs

Population-level effects of suppressing fever

Epidemic fronts in complex networks with metapopulation structure

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