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Exact Equations for SIR Epidemics on Tree Graphs.

Sharkey KJ, Kiss IZ, Wilkinson RR, Simon PL - Bull. Math. Biol. (2013)

Bottom Line: We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected.We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph.Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK, kjs@liv.ac.uk.

ABSTRACT
We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

No MeSH data available.


Related in: MedlinePlus

Each box illustrates the relevant node states for the four parts of the closure relation in the equation above it. The node states on the left and the right correspond to the two terms in the closure relation. The node numbers correspond to the same positions as in Fig. 4
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Fig5: Each box illustrates the relevant node states for the four parts of the closure relation in the equation above it. The node states on the left and the right correspond to the two terms in the closure relation. The node numbers correspond to the same positions as in Fig. 4

Mentions: The closure relations each consist of two pairs which are visualised in Fig. 5. For reference, we refer to these as the left pair and the right pair referring to their position in this figure. Looking at these closure relations, we can form two observations:


Exact Equations for SIR Epidemics on Tree Graphs.

Sharkey KJ, Kiss IZ, Wilkinson RR, Simon PL - Bull. Math. Biol. (2013)

Each box illustrates the relevant node states for the four parts of the closure relation in the equation above it. The node states on the left and the right correspond to the two terms in the closure relation. The node numbers correspond to the same positions as in Fig. 4
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC4541714&req=5

Fig5: Each box illustrates the relevant node states for the four parts of the closure relation in the equation above it. The node states on the left and the right correspond to the two terms in the closure relation. The node numbers correspond to the same positions as in Fig. 4
Mentions: The closure relations each consist of two pairs which are visualised in Fig. 5. For reference, we refer to these as the left pair and the right pair referring to their position in this figure. Looking at these closure relations, we can form two observations:

Bottom Line: We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected.We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph.Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

View Article: PubMed Central - PubMed

Affiliation: Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZL, UK, kjs@liv.ac.uk.

ABSTRACT
We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where network links may be directed or undirected. We prove that a particular pair-based moment closure representation generates the expected infectious time series for networks with no cycles in the underlying graph. Moreover, this "deterministic" representation of the expected behaviour of a complex heterogeneous and finite Markovian system is straightforward to evaluate numerically.

No MeSH data available.


Related in: MedlinePlus