Mean-field-like approximations for stochastic processes on weighted and dynamic networks

Rattana, Prapanporn (2015) Mean-field-like approximations for stochastic processes on weighted and dynamic networks. Doctoral thesis (PhD), University of Sussex.

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The explicit use of networks in modelling stochastic processes such as epidemic dynamics
has revolutionised research into understanding the impact of contact pattern
properties, such as degree heterogeneity, preferential mixing, clustering, weighted and
dynamic linkages, on how epidemics invade, spread and how to best control them. In
this thesis, I worked on mean-field approximations of stochastic processes on networks
with particular focus on weighted and dynamic networks. I mostly used low dimensional
ordinary differential equation (ODE) models and explicit network-based stochastic simulations to model and analyse how epidemics become established and spread in weighted and dynamic networks.

I begin with a paper presenting the susceptible-infected-susceptible/recovered (SIS,
SIR) epidemic models on static weighted networks with different link weight distributions.
This work extends the pairwise model paradigm to weighted networks and gives
excellent agreement with simulations. The basic reproductive ratio, R0, is formulated
for SIR dynamics. The effects of link weight distribution on R0 and on the spread of
the disease are investigated in detail. This work is followed by a second paper, which
considers weighted networks in which the nodal degree and weights are not independent.
Moreover, two approximate models are explored: (i) the pairwise model and (ii)
the edge-based compartmental model. These are used to derive important epidemic
descriptors, including early growth rate, final epidemic size, basic reproductive ratio
and epidemic dynamics. Whilst the first two papers concentrate on static networks,
the third paper focuses on dynamic networks, where links can be activated and/or
deleted and this process can evolve together with the epidemic dynamics. We consider
an adaptive network with a link rewiring process constrained by spatial proximity. This
model couples SIS dynamics with that of the network and it investigates the impact of rewiring on the network structure and disease die-out induced by the rewiring process.
The fourth paper shows that the generalised master equations approach works well for
networks with low degree heterogeneity but it fails to capture networks with modest
or high degree heterogeneity. In particular, we show that a recently proposed generalisation
performs poorly, except for networks with low heterogeneity and high average

Item Type: Thesis (Doctoral)
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Subjects: Q Science > QA Mathematics > QA0273 Probabilities. Mathematical statistics
Depositing User: Library Cataloguing
Date Deposited: 14 Sep 2015 08:11
Last Modified: 14 Sep 2015 08:11

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