53 citations · 167 across the 9 of their papers we have counts for
10 papers
Deterministic epidemic models overestimate the basic reproduction number of observed outbreaks
Wajid Ali, Christopher E. Overton, Robert R. Wilkinson +1
The basic reproduction number, , is a well-known quantifier of epidemic spread. However, a class of existing methods for estimating from incidence data early in the epid…
Approximating quasi-stationary behaviour in network-based SIS dynamics
Christopher E. Overton, Robert R. Wilkinson, Adedapo Loyinmi +2
Deterministic approximations to stochastic Susceptible-Infectious-Susceptible models typically predict a stable endemic steady-state when above threshold. This can be hard to relat…
Impact of the infectious period on epidemics
Robert R. Wilkinson, Kieran J. Sharkey
The duration of the infectious period is a crucial determinant of the ability of an infectious disease to spread. We consider an epidemic model that is network based and non-Markov…
The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models
Robert R. Wilkinson, Frank G. Ball, Kieran J. Sharkey
We consider a very general stochastic model for an SIR epidemic on a network which allows an individual's infectious period, and the time it takes to contact each of its neighbours…
The deterministic Kermack-McKendrick model bounds the general stochastic epidemic
Robert R. Wilkinson, Frank G. Ball, Kieran J. Sharkey
We prove that, for Poisson transmission and recovery processes, the classic Susceptible Infected Recovered (SIR) epidemic model of Kermack and McKendrick provides, for…
Intrinsic Contractivity of Feynman-Kac Semigroups for Symmetric Jump Processes with Infinite Range Jumps
Xin Chen, Jian Wang
Let be a symmetric strong Markov process generated by non-local regular Dirichlet form $(D,\D(D))$ as follows \begin{equation*} \begin{split} & D(f,g)=\int_{\R^d}\…
Message passing and moment closure for susceptible-infected-recovered epidemics on finite networks
Robert R. Wilkinson, Kieran J. Sharkey
The message passing approach of Karrer and Newman [Phys. Rev. E 82, 016101 (2010)] is an exact and practicable representation of susceptible-infected-recovered dynamics on finite t…
Exact deterministic representation of Markovian SIR epidemics on networks with and without loops
Istvan Z. Kiss, Charles G. Morris, Fanni Sélley +2
In a previous paper Sharkey et al. [13] proved the exactness of closures at the level of triples for Markovian SIR (susceptible-infected-removed) dynamics on tree-like networks. Th…
An Exact Relationship Between Invasion Probability and Endemic Prevalence for Markovian SIS Dynamics on Networks
Robert R. Wilkinson, Kieran J. Sharkey
Understanding models which represent the invasion of network-based systems by infectious agents can give important insights into many real-world situations, including the preventio…
Exact equations for SIR epidemics on tree graphs
Kieran J. Sharkey, Istvan Z. Kiss, Robert R. Wilkinson +1
We consider Markovian susceptible-infectious-removed (SIR) dynamics on time-invariant weighted contact networks where the infection and removal processes are Poisson and where netw…