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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 circle refers to one of the motif states , , ,  specified to the top left. The position of the relevant node states with respect to the motif states are then illustrated. (a) Subcase 1.1 (n∉Y). (b) Subcase 1.2 (n∈Y)
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Fig6: Each circle refers to one of the motif states , , , specified to the top left. The position of the relevant node states with respect to the motif states are then illustrated. (a) Subcase 1.1 (n∉Y). (b) Subcase 1.2 (n∈Y)

Mentions: We have Aw=S, and n∉W. Let us now identify a term in to form compatible pairs. According to CP(i) and CP(ii) we can assume without loss of generality that Ww∈Y, i.e. ∃y:Yy=Ww and Cy=S (see Fig. 6). There are two subcases: Fig. 6


Exact Equations for SIR Epidemics on Tree Graphs.

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

Each circle refers to one of the motif states , , ,  specified to the top left. The position of the relevant node states with respect to the motif states are then illustrated. (a) Subcase 1.1 (n∉Y). (b) Subcase 1.2 (n∈Y)
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Related In: Results  -  Collection

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Fig6: Each circle refers to one of the motif states , , , specified to the top left. The position of the relevant node states with respect to the motif states are then illustrated. (a) Subcase 1.1 (n∉Y). (b) Subcase 1.2 (n∈Y)
Mentions: We have Aw=S, and n∉W. Let us now identify a term in to form compatible pairs. According to CP(i) and CP(ii) we can assume without loss of generality that Ww∈Y, i.e. ∃y:Yy=Ww and Cy=S (see Fig. 6). There are two subcases: Fig. 6

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