## Ball, Frank G.

Compute Distance To:
 Author ID: ball.frank-g Published as: Ball, Frank; Ball, Frank G.; Ball, F.; Ball, F. G. more...less Homepage: https://www.nottingham.ac.uk/mathematics/people/frank.ball External Links: MGP · Math-Net.Ru · dblp
 Documents Indexed: 103 Publications since 1983 Co-Authors: 43 Co-Authors with 85 Joint Publications 770 Co-Co-Authors
all top 5

### Co-Authors

 18 single-authored 12 Britton, Tom 12 Sirl, David J. 10 Milne, Robin K. 10 Yeo, Geoffrey F. 8 O’Neill, Philip D. 8 Trapman, Pieter 6 Lyne, Owen D. 6 Neal, Peter J. 3 Clancy, Damian 3 Donnelly, Peter 3 Knock, Edward S. 3 Stefanov, Valeri T. 2 Donelly, P. 2 Gonzalez-Velasco, Miguel 2 Martínez, Rodrigo 2 Pellis, Lorenzo 2 Rice, John A. 2 Sansom, Mark 2 Sharkey, Kieran J. 2 Shaw, Laurence 2 Slavtchova-Bojkova, Maroussia Nikiforova 2 Wilkinson, Robert R. 1 Barbour, Andrew David 1 Becker, Niels G. 1 Blackwell, Paul G. 1 Davies, S. S. 1 Davies, Sue 1 Dryden, Ian L. 1 Dunham, Bruce 1 Golalizadeh, Mousa 1 Hirschowitz, André 1 House, Thomas 1 Kadane, Joseph Born 1 Leung, Ka Yin 1 Mollison, Denis 1 Nåsell, Ingemar 1 O’Hagan, Anthony 1 Pike, James 1 Scalia Tomba, Gianpaolo 1 Smith, Adrian F. M. 1 Tame, Ian D. 1 Verdinelli, Isabella 1 Winch, Tom
all top 5

### Serials

 20 Advances in Applied Probability 20 Journal of Applied Probability 18 Mathematical Biosciences 7 Journal of Mathematical Biology 5 The Annals of Applied Probability 3 Methodology and Computing in Applied Probability 2 Biometrika 2 IMA Journal of Mathematics Applied in Medicine and Biology 2 Stochastic Processes and their Applications 1 Journal of Mathematical Analysis and Applications 1 Teoriya Veroyatnosteĭ i eë Primeneniya 1 Theory of Probability and its Applications 1 The Annals of Probability 1 Biometrics 1 Journal of Statistical Planning and Inference 1 The Mathematical Scientist 1 Communications in Statistics. Stochastic Models 1 Journal of the Royal Statistical Society. Series B 1 Bernoulli 1 Journal of Applied Mathematics and Decision Sciences 1 Australian & New Zealand Journal of Statistics 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 1 Statistical Methods in Medical Research 1 Mathematical Medicine and Biology 1 Science
all top 5

### Fields

 88 Biology and other natural sciences (92-XX) 81 Probability theory and stochastic processes (60-XX) 16 Combinatorics (05-XX) 11 Numerical analysis (65-XX) 9 Statistics (62-XX) 4 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Systems theory; control (93-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Special functions (33-XX) 1 Ordinary differential equations (34-XX) 1 Operations research, mathematical programming (90-XX)

### Citations contained in zbMATH Open

89 Publications have been cited 1,075 times in 553 Documents Cited by Year
Epidemics with two levels of mixing. Zbl 0909.92028
Ball, Frank; Mollison, Denis; Scalia-Tomba, Gianpaolo
1997
Strong approximations for epidemic models. Zbl 0823.92024
Ball, Frank; Donnelly, Peter
1995
The threshold behaviour of epidemic models. Zbl 0519.92023
Ball, Frank
1983
A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Zbl 0606.92018
Ball, Frank
1986
A general model for stochastic SIR epidemics with two levels of mixing. Zbl 1015.92034
Ball, Frank; Neal, Peter
2002
Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Zbl 1192.92037
Ball, Frank; Sirl, David; Trapman, Pieter
2010
Network epidemic models with two levels of mixing. Zbl 1132.92020
Ball, Frank; Neal, Peter
2008
Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Zbl 0979.92033
Ball, Frank
1999
Stochastic multitype SIR epidemics among a population partitioned into households. Zbl 0978.92025
Ball, Frank; Lyne, Owen D.
2001
Threshold behaviour and final outcome of an epidemic on a random network with household structure. Zbl 1176.92042
Ball, Frank; Sirl, David; Trapman, Pieter
2009
Reproduction numbers for epidemic models with households and other social structures. I: Definition and calculation of $$R_{0}$$. Zbl 1241.92067
Pellis, Lorenzo; Ball, Frank; Trapman, Pieter
2012
The final size and severity of a generalised stochastic multitype epidemic model. Zbl 0798.92025
Ball, Frank; Clancy, Damian
1993
The distribution of general final state random variables for stochastic epidemic models. Zbl 0940.92021
Ball, Frank; O’Neill, Philip
1999
Deterministic and stochastic epidemics with several kinds of susceptibles. Zbl 0571.92019
Ball, Frank
1985
Optimal vaccination policies for stochastic epidemics among a population of households. Zbl 0996.92032
Ball, Frank G.; Lyne, Owen D.
2002
An SIR epidemic model on a population with random network and household structure, and several types of individuals. Zbl 1236.92043
Ball, Frank; Sirl, David
2012
Epidemics on random intersection graphs. Zbl 1291.92098
Ball, Frank G.; Sirl, David J.; Trapman, Pieter
2014
A modification of the general stochastic epidemic motivated by AIDS modelling. Zbl 0777.92018
Ball, Frank; O’Neill, Philip
1993
Lumpability and marginalisability for continuous-time Markov chains. Zbl 0781.60057
Ball, Frank; Yeo, Geoffrey F.
1993
The final outcome of an epidemic model with several different types of infective in a large population. Zbl 0844.92019
Ball, Frank; Clancy, Damian
1995
Threshold behaviour in stochastic epidemics among households. Zbl 0854.92015
Ball, Frank
1996
Stochastic multitype epidemics in a community of households: estimation of threshold parameter $$R_ *$$ and secure vaccination coverage. Zbl 1079.62101
Ball, Frank G.; Britton, Tom; Lyne, Owen D.
2004
Dynamic population epidemic models. Zbl 0747.92025
Ball, Frank G.
1991
The great circle epidemic model. Zbl 1075.60565
Ball, Frank; Neal, Peter
2003
Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes. Zbl 1073.92041
Ball, Frank; Britton, Tom; Lyne, Owen
2004
Stochastic models for ion channels: Introduction and bibliography. Zbl 0767.92007
Ball, Frank G.; Rice, John A.
1992
Aggregated semi-Markov processes incorporating time interval omission. Zbl 0748.60088
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1991
A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon. Zbl 1258.92031
Ball, Frank; Britton, Tom; Sirl, David
2013
An epidemic model with exposure-dependent severities. Zbl 1090.92041
Ball, Frank; Britton, Tom
2005
A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2. Zbl 1478.92180
Britton, Tom; Ball, Frank; Trapman, Pieter
2020
Reproduction numbers for epidemic models with households and other social structures. II: comparisons and implications for vaccination. Zbl 1365.92115
Ball, Frank; Pellis, Lorenzo; Trapman, Pieter
2016
A note on variation in birth processes. Zbl 0824.60076
Ball, Frank
1995
Stochastic epidemic models in structured populations featuring dynamic vaccination and isolation. Zbl 1128.92035
Ball, Frank; O’Neill, Philip D.; Pike, James
2007
An epidemic model with infector-dependent severity. Zbl 1130.92045
Ball, Frank; Britton, Tom
2007
Control of transmission with two types of infection. Zbl 1089.92028
Ball, Frank; Becker, Niels G.
2006
A threshold theorem for the Reed-Frost chain-binomial epidemic. Zbl 0505.92020
Ball, Frank
1983
Continuous-time Markov chains in a random environment, with applications to ion channel modelling. Zbl 0812.60061
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1994
Biased coin designs with a Bayesian bias. Zbl 0783.62054
Ball, F. G.; Smith, A. F. M.; Verdinelli, I.
1993
Heterogeneous network epidemics: real-time growth, variance and extinction of infection. Zbl 1377.92080
Ball, Frank; House, Thomas
2017
Acquaintance vaccination in an epidemic on a random graph with specified degree distribution. Zbl 1301.92071
Ball, Frank; Sirl, David
2013
Threshold behaviour of emerging epidemics featuring contact tracing. Zbl 1229.92067
Ball, Frank G.; Knock, Edward S.; O’Neill, Philip D.
2011
A stochastic SIR network epidemic model with preventive dropping of edges. Zbl 1415.92167
Ball, Frank; Britton, Tom; Leung, Ka Yin; Sirl, David
2019
Control of emerging infectious diseases using responsive imperfect vaccination and isolation. Zbl 1151.92028
Ball, Frank G.; Knock, Edward S.; O’Neill, Philip D.
2008
Bayesian inference for ion-channel gating mechanisms directly from single-channel recordings, using Markov chain Monte Carlo. Zbl 1063.62586
Ball, F. G.; Cai, Y.; Kadane, J. B.; O’Hagan, A.
1999
Poisson approximation for some epidemic models. Zbl 0753.60013
Ball, Frank; Barbour, A. D.
1990
Optimal vaccination schemes for epidemics among a population of households, with application to variola minor in Brazil. Zbl 1122.92303
Ball, Frank; Lyne, Owen
2006
The shape of the size distribution of an epidemic in a finite population. Zbl 0805.92023
Ball, Frank; Nåsell, Ingemar
1994
Stochastic models for systems of interacting ion channels. Zbl 0968.92008
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2000
Poisson approximations for epidemics with two levels of mixing. Zbl 1060.92050
Ball, Frank; Neal, Peter
2004
Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure. Zbl 1392.92092
Ball, Frank; Sirl, David
2018
The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models. Zbl 1383.92090
Wilkinson, Robert R.; Ball, Frank G.; Sharkey, Kieran J.
2017
On expected durations of birth-death processes, with applications to branching processes and SIS epidemics. Zbl 1337.60207
Ball, Frank; Britton, Tom; Neal, Peter
2016
Multivariate semi-Markov analysis of burst properties of multiconductance single ion channels. Zbl 1001.92006
Ball, F.; Milne, R. K.; Yeo, G. F.
2002
Strong convergence of stochastic epidemics. Zbl 0812.92018
Ball, Frank; O’Neill, Philip
1994
Empirical clustering of bursts of openings in Markov and semi-Markov models of single channel gating incorporating time interval omission. Zbl 0903.60058
Ball, Frank
1997
Interparticle correlation in death processes with application to variability in compartmental models. Zbl 0634.60074
Ball, Frank; Donnelly, Peter
1987
An epidemic model with infector and exposure dependent severity. Zbl 1160.92034
Ball, Frank; Britton, Tom
2009
The asymptotic variance of the giant component of configuration model random graphs. Zbl 1367.05192
Ball, Frank; Neal, Peter
2017
Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling. Zbl 1329.60299
Ball, Frank; González, Miguel; Martínez, Rodrigo; Slavtchova-Bojkova, Maroussia
2014
Further approaches to computing fundamental characteristics of birth-death processes. Zbl 0995.60074
Ball, Frank; Stefanov, Valeri T.
2001
On the exact distribution of observed open times in single ion channel models. Zbl 0781.60076
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1993
Statistical inference for a two-state Markov model of a single ion channel, incorporating time interval omission. Zbl 0809.62076
Ball, F. G.; Davies, S. S.
1995
Central limit theorems for multivariate semi-Markov sequences and processes, with applications. Zbl 0955.60086
Ball, Frank
1999
Aggregated Markov processes incorporating time interval omission. Zbl 0654.60077
Ball, Frank; Sansom, Mark
1988
Epidemics among a population of households. Zbl 1022.92026
Ball, Frank G.; Lyne, Owen D.
2002
Stochastic epidemic models featuring contact tracing with delays. Zbl 1356.92077
Ball, Frank G.; Knock, Edward S.; O’Neill, Philip D.
2015
Simple derivations of properties of counting processes associated with Markov renewal processes. Zbl 1106.60069
Ball, Frank; Milne, Robin K.
2005
Susceptibility sets and the final outcome of collective Reed-Frost epidemics. Zbl 1429.92123
Ball, Frank
2019
Superposition of spatially interacting aggregated continuous time Markov chains. Zbl 0959.92004
Ball, Frank; Yeo, Geoffrey
2000
The final outcome and temporal solution of a carrier-borne epidemic model. Zbl 0822.92017
Ball, Frank; Clancy, Damian
1995
Coupling methods in epidemic theory. Zbl 0838.92020
Ball, Frank
1995
Applications of simple point process methods to superpositions of aggregated stationary processes. Zbl 1078.60037
Ball, Frank G.; Milne, Robin K.
2004
Evaluation of identity-by-descent probabilities for half-sibs on continuous genome. Zbl 1070.92035
Ball, Frank; Stefanov, Valeri T.
2005
Temporal clustering of ion channel openings incorporating time interval omission. Zbl 0642.92001
Ball, Frank; Sansom, Mark
1987
Branching process approximation of epidemic models. Zbl 0794.92019
Ball, F.; Donelly, P.
1992
The deterministic Kermack-McKendrick model bounds the general stochastic epidemic. Zbl 1353.92105
Wilkinson, Robert R.; Ball, Frank G.; Sharkey, Kieran J.
2016
Marked continuous-time Markov chain modelling of burst behaviour for single ion channels. Zbl 1211.92007
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2007
Aggregated Markov processes with negative exponential time interval omission. Zbl 0726.60070
Ball, Frank
1990
Superposition of interacting aggregated continuous-time Markov chains. Zbl 0873.60051
Ball, Frank; Milne, Robin K.; Tame, Ian D.; Yeo, Geoffrey F.
1997
Clustering of bursts of openings in Markov and semi-Markov models of single channel gating. Zbl 0874.60069
Ball, Frank; Davies, Sue
1997
A note on the total size distribution of epidemic models. Zbl 0599.92015
Ball, Frank
1986
A unified approach to burst properties of multiconductance single ion channels. Zbl 1055.92015
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2004
The threshold behaviour of stochastic epidemics. Zbl 0930.92019
Ball, Frank
1997
Estimating the within-household infection rate in emerging SIR epidemics among a community of households. Zbl 1356.92078
Ball, Frank; Shaw, Laurence
2015
Branching process approximation of epidemic models. Zbl 0762.92016
Ball, F.; Donelly, P.
1992
Empty confidence sets for epidemics, branching processes and Brownian motion. Zbl 0997.62059
Ball, Frank G.; Britton, Tom; O’Neill, Philip D.
2002
Brownian motion and Ornstein-Uhlenbeck processes in planar shape space. Zbl 1145.60327
Ball, Frank G.; Dryden, Ian L.; Golalizadeh, Mousa
2008
A note on single-channel autocorrelation functions. Zbl 0679.92009
Ball, Frank G.; Rice, John A.
1989
Stochastic SIR epidemics in structured populations. Zbl 1447.92394
Ball, Frank; Sirl, David
2019
A mathematical model reveals the influence of population heterogeneity on herd immunity to SARS-CoV-2. Zbl 1478.92180
Britton, Tom; Ball, Frank; Trapman, Pieter
2020
A stochastic SIR network epidemic model with preventive dropping of edges. Zbl 1415.92167
Ball, Frank; Britton, Tom; Leung, Ka Yin; Sirl, David
2019
Susceptibility sets and the final outcome of collective Reed-Frost epidemics. Zbl 1429.92123
Ball, Frank
2019
Stochastic SIR epidemics in structured populations. Zbl 1447.92394
Ball, Frank; Sirl, David
2019
Evaluation of vaccination strategies for SIR epidemics on random networks incorporating household structure. Zbl 1392.92092
Ball, Frank; Sirl, David
2018
Heterogeneous network epidemics: real-time growth, variance and extinction of infection. Zbl 1377.92080
Ball, Frank; House, Thomas
2017
The relationships between message passing, pairwise, Kermack-McKendrick and stochastic SIR epidemic models. Zbl 1383.92090
Wilkinson, Robert R.; Ball, Frank G.; Sharkey, Kieran J.
2017
The asymptotic variance of the giant component of configuration model random graphs. Zbl 1367.05192
Ball, Frank; Neal, Peter
2017
Reproduction numbers for epidemic models with households and other social structures. II: comparisons and implications for vaccination. Zbl 1365.92115
Ball, Frank; Pellis, Lorenzo; Trapman, Pieter
2016
On expected durations of birth-death processes, with applications to branching processes and SIS epidemics. Zbl 1337.60207
Ball, Frank; Britton, Tom; Neal, Peter
2016
The deterministic Kermack-McKendrick model bounds the general stochastic epidemic. Zbl 1353.92105
Wilkinson, Robert R.; Ball, Frank G.; Sharkey, Kieran J.
2016
Stochastic epidemic models featuring contact tracing with delays. Zbl 1356.92077
Ball, Frank G.; Knock, Edward S.; O&rsquo;Neill, Philip D.
2015
Estimating the within-household infection rate in emerging SIR epidemics among a community of households. Zbl 1356.92078
Ball, Frank; Shaw, Laurence
2015
Epidemics on random intersection graphs. Zbl 1291.92098
Ball, Frank G.; Sirl, David J.; Trapman, Pieter
2014
Stochastic monotonicity and continuity properties of functions defined on Crump-Mode-Jagers branching processes, with application to vaccination in epidemic modelling. Zbl 1329.60299
Ball, Frank; González, Miguel; Martínez, Rodrigo; Slavtchova-Bojkova, Maroussia
2014
A network with tunable clustering, degree correlation and degree distribution, and an epidemic thereon. Zbl 1258.92031
Ball, Frank; Britton, Tom; Sirl, David
2013
Acquaintance vaccination in an epidemic on a random graph with specified degree distribution. Zbl 1301.92071
Ball, Frank; Sirl, David
2013
Reproduction numbers for epidemic models with households and other social structures. I: Definition and calculation of $$R_{0}$$. Zbl 1241.92067
Pellis, Lorenzo; Ball, Frank; Trapman, Pieter
2012
An SIR epidemic model on a population with random network and household structure, and several types of individuals. Zbl 1236.92043
Ball, Frank; Sirl, David
2012
Threshold behaviour of emerging epidemics featuring contact tracing. Zbl 1229.92067
Ball, Frank G.; Knock, Edward S.; O&rsquo;Neill, Philip D.
2011
Analysis of a stochastic SIR epidemic on a random network incorporating household structure. Zbl 1192.92037
Ball, Frank; Sirl, David; Trapman, Pieter
2010
Threshold behaviour and final outcome of an epidemic on a random network with household structure. Zbl 1176.92042
Ball, Frank; Sirl, David; Trapman, Pieter
2009
An epidemic model with infector and exposure dependent severity. Zbl 1160.92034
Ball, Frank; Britton, Tom
2009
Network epidemic models with two levels of mixing. Zbl 1132.92020
Ball, Frank; Neal, Peter
2008
Control of emerging infectious diseases using responsive imperfect vaccination and isolation. Zbl 1151.92028
Ball, Frank G.; Knock, Edward S.; O&rsquo;Neill, Philip D.
2008
Brownian motion and Ornstein-Uhlenbeck processes in planar shape space. Zbl 1145.60327
Ball, Frank G.; Dryden, Ian L.; Golalizadeh, Mousa
2008
Stochastic epidemic models in structured populations featuring dynamic vaccination and isolation. Zbl 1128.92035
Ball, Frank; O&rsquo;Neill, Philip D.; Pike, James
2007
An epidemic model with infector-dependent severity. Zbl 1130.92045
Ball, Frank; Britton, Tom
2007
Marked continuous-time Markov chain modelling of burst behaviour for single ion channels. Zbl 1211.92007
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2007
Control of transmission with two types of infection. Zbl 1089.92028
Ball, Frank; Becker, Niels G.
2006
Optimal vaccination schemes for epidemics among a population of households, with application to variola minor in Brazil. Zbl 1122.92303
Ball, Frank; Lyne, Owen
2006
An epidemic model with exposure-dependent severities. Zbl 1090.92041
Ball, Frank; Britton, Tom
2005
Simple derivations of properties of counting processes associated with Markov renewal processes. Zbl 1106.60069
Ball, Frank; Milne, Robin K.
2005
Evaluation of identity-by-descent probabilities for half-sibs on continuous genome. Zbl 1070.92035
Ball, Frank; Stefanov, Valeri T.
2005
Stochastic multitype epidemics in a community of households: estimation of threshold parameter $$R_ *$$ and secure vaccination coverage. Zbl 1079.62101
Ball, Frank G.; Britton, Tom; Lyne, Owen D.
2004
Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes. Zbl 1073.92041
Ball, Frank; Britton, Tom; Lyne, Owen
2004
Poisson approximations for epidemics with two levels of mixing. Zbl 1060.92050
Ball, Frank; Neal, Peter
2004
Applications of simple point process methods to superpositions of aggregated stationary processes. Zbl 1078.60037
Ball, Frank G.; Milne, Robin K.
2004
A unified approach to burst properties of multiconductance single ion channels. Zbl 1055.92015
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2004
The great circle epidemic model. Zbl 1075.60565
Ball, Frank; Neal, Peter
2003
A general model for stochastic SIR epidemics with two levels of mixing. Zbl 1015.92034
Ball, Frank; Neal, Peter
2002
Optimal vaccination policies for stochastic epidemics among a population of households. Zbl 0996.92032
Ball, Frank G.; Lyne, Owen D.
2002
Multivariate semi-Markov analysis of burst properties of multiconductance single ion channels. Zbl 1001.92006
Ball, F.; Milne, R. K.; Yeo, G. F.
2002
Epidemics among a population of households. Zbl 1022.92026
Ball, Frank G.; Lyne, Owen D.
2002
Empty confidence sets for epidemics, branching processes and Brownian motion. Zbl 0997.62059
Ball, Frank G.; Britton, Tom; O&rsquo;Neill, Philip D.
2002
Stochastic multitype SIR epidemics among a population partitioned into households. Zbl 0978.92025
Ball, Frank; Lyne, Owen D.
2001
Further approaches to computing fundamental characteristics of birth-death processes. Zbl 0995.60074
Ball, Frank; Stefanov, Valeri T.
2001
Stochastic models for systems of interacting ion channels. Zbl 0968.92008
Ball, Frank G.; Milne, Robin K.; Yeo, Geoffrey F.
2000
Superposition of spatially interacting aggregated continuous time Markov chains. Zbl 0959.92004
Ball, Frank; Yeo, Geoffrey
2000
Stochastic and deterministic models for SIS epidemics among a population partitioned into households. Zbl 0979.92033
Ball, Frank
1999
The distribution of general final state random variables for stochastic epidemic models. Zbl 0940.92021
Ball, Frank; O&rsquo;Neill, Philip
1999
Bayesian inference for ion-channel gating mechanisms directly from single-channel recordings, using Markov chain Monte Carlo. Zbl 1063.62586
Ball, F. G.; Cai, Y.; Kadane, J. B.; O&rsquo;Hagan, A.
1999
Central limit theorems for multivariate semi-Markov sequences and processes, with applications. Zbl 0955.60086
Ball, Frank
1999
Epidemics with two levels of mixing. Zbl 0909.92028
Ball, Frank; Mollison, Denis; Scalia-Tomba, Gianpaolo
1997
Empirical clustering of bursts of openings in Markov and semi-Markov models of single channel gating incorporating time interval omission. Zbl 0903.60058
Ball, Frank
1997
Superposition of interacting aggregated continuous-time Markov chains. Zbl 0873.60051
Ball, Frank; Milne, Robin K.; Tame, Ian D.; Yeo, Geoffrey F.
1997
Clustering of bursts of openings in Markov and semi-Markov models of single channel gating. Zbl 0874.60069
Ball, Frank; Davies, Sue
1997
The threshold behaviour of stochastic epidemics. Zbl 0930.92019
Ball, Frank
1997
Threshold behaviour in stochastic epidemics among households. Zbl 0854.92015
Ball, Frank
1996
Strong approximations for epidemic models. Zbl 0823.92024
Ball, Frank; Donnelly, Peter
1995
The final outcome of an epidemic model with several different types of infective in a large population. Zbl 0844.92019
Ball, Frank; Clancy, Damian
1995
A note on variation in birth processes. Zbl 0824.60076
Ball, Frank
1995
Statistical inference for a two-state Markov model of a single ion channel, incorporating time interval omission. Zbl 0809.62076
Ball, F. G.; Davies, S. S.
1995
The final outcome and temporal solution of a carrier-borne epidemic model. Zbl 0822.92017
Ball, Frank; Clancy, Damian
1995
Coupling methods in epidemic theory. Zbl 0838.92020
Ball, Frank
1995
Continuous-time Markov chains in a random environment, with applications to ion channel modelling. Zbl 0812.60061
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1994
The shape of the size distribution of an epidemic in a finite population. Zbl 0805.92023
Ball, Frank; Nåsell, Ingemar
1994
Strong convergence of stochastic epidemics. Zbl 0812.92018
Ball, Frank; O&rsquo;Neill, Philip
1994
The final size and severity of a generalised stochastic multitype epidemic model. Zbl 0798.92025
Ball, Frank; Clancy, Damian
1993
A modification of the general stochastic epidemic motivated by AIDS modelling. Zbl 0777.92018
Ball, Frank; O&rsquo;Neill, Philip
1993
Lumpability and marginalisability for continuous-time Markov chains. Zbl 0781.60057
Ball, Frank; Yeo, Geoffrey F.
1993
Biased coin designs with a Bayesian bias. Zbl 0783.62054
Ball, F. G.; Smith, A. F. M.; Verdinelli, I.
1993
On the exact distribution of observed open times in single ion channel models. Zbl 0781.60076
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1993
Stochastic models for ion channels: Introduction and bibliography. Zbl 0767.92007
Ball, Frank G.; Rice, John A.
1992
Branching process approximation of epidemic models. Zbl 0794.92019
Ball, F.; Donelly, P.
1992
Branching process approximation of epidemic models. Zbl 0762.92016
Ball, F.; Donelly, P.
1992
Dynamic population epidemic models. Zbl 0747.92025
Ball, Frank G.
1991
Aggregated semi-Markov processes incorporating time interval omission. Zbl 0748.60088
Ball, Frank; Milne, Robin K.; Yeo, Geoffrey F.
1991
Poisson approximation for some epidemic models. Zbl 0753.60013
Ball, Frank; Barbour, A. D.
1990
Aggregated Markov processes with negative exponential time interval omission. Zbl 0726.60070
Ball, Frank
1990
A note on single-channel autocorrelation functions. Zbl 0679.92009
Ball, Frank G.; Rice, John A.
1989
Aggregated Markov processes incorporating time interval omission. Zbl 0654.60077
Ball, Frank; Sansom, Mark
1988
Interparticle correlation in death processes with application to variability in compartmental models. Zbl 0634.60074
Ball, Frank; Donnelly, Peter
1987
Temporal clustering of ion channel openings incorporating time interval omission. Zbl 0642.92001
Ball, Frank; Sansom, Mark
1987
A unified approach to the distribution of total size and total area under the trajectory of infectives in epidemic models. Zbl 0606.92018
Ball, Frank
1986
A note on the total size distribution of epidemic models. Zbl 0599.92015
Ball, Frank
1986
Deterministic and stochastic epidemics with several kinds of susceptibles. Zbl 0571.92019
Ball, Frank
1985
The threshold behaviour of epidemic models. Zbl 0519.92023
Ball, Frank
1983
A threshold theorem for the Reed-Frost chain-binomial epidemic. Zbl 0505.92020
Ball, Frank
1983
all top 5

### Cited by 877 Authors

 43 Ball, Frank G. 28 Britton, Tom 22 Lefèvre, Claude 21 Neal, Peter J. 17 Kiss, István Z. 17 O’Neill, Philip D. 17 Trapman, Pieter 13 Clancy, Damian 13 Picard, Philippe 12 House, Thomas 10 Simon, Peter L. 8 Becker, Niels G. 8 Jin, Zhen 8 Ma, Junling 8 Ross, Joshua V. 8 Sirl, David J. 7 Barbour, Andrew David 7 Berthouze, Luc 7 Faddy, Malcolm J. 6 Artalejo, Jesus R. 6 Leung, Ka Yin 6 Li, Wenxue 6 Miller, Joel C. 5 Allen, Linda J. S. 5 Black, Andrew J. 5 Cui, Lirong 5 Gomes, M. Gabriela M. 5 Gonzalez-Velasco, Miguel 5 Lopez-Herrero, Maria Jesus 5 Martínez, Rodrigo 5 Pellis, Lorenzo 5 Sharkey, Kieran J. 5 Simon, Matthieu 5 Spencer, Simon Edward Frank 5 Utev, Sergey 5 van den Driessche, Pauline 4 Barnes, Belinda 4 Economou, Antonis 4 Glass, Kathryn 4 Komjáthy, Júlia 4 Kretzschmar, Mirjam 4 Milne, Robin K. 4 Slavtchova-Bojkova, Maroussia Nikiforova 4 Wang, Ke 4 Wang, Liying 4 Wang, Weiming 4 Wilkinson, Robert R. 4 Yuan, Sanling 3 Atkinson, Anthony C. 3 Bean, Nigel G. 3 Biswas, Atanu 3 Cai, Yongli 3 Chen, Shihua 3 Diekmann, Odo 3 Ephraim, Yariv 3 Fuh, Cheng-Der 3 Gao, Shujing 3 Hiebeler, David E. 3 Janson, Svante 3 Knock, Edward S. 3 Kypraios, Theodore 3 Lindholm, Mathias 3 Luczak, Malwina J. 3 Lyne, Owen D. 3 Mark, Brian L. 3 Mode, Charles J. 3 Müller, Johannes 3 Rebelo, Carlota 3 Reinert, Gesine D. 3 Sleeman, Candace K. 3 van der Hofstad, Remco W. 3 Willeboordse, Frederick H. 3 Yeo, Geoffrey F. 3 Zhang, Juping 3 Zhang, Yan 2 Andreasen, Viggo 2 Aparicio, Juan Pablo 2 Bacaër, Nicolas 2 Balakrishnan, Narayanaswamy 2 Balcan, Duygu 2 Barnard, Rosanna C. 2 Bielecki, Tomasz R. 2 Blyuss, Konstantin B. 2 Bosch, Ronald J. 2 Clementi, Andrea E. F. 2 Colizza, Vittoria 2 Corder, Rodrigo M. 2 de Gunst, Mathisca C. M. 2 Deijfen, Maria 2 Dekker, Rommert 2 Demiris, Nikolaos 2 Dietz, Klaus 2 Donnelly, Peter 2 Draief, Moez 2 Durrett, Richard Timothy 2 Eames, Ken T. D. 2 Edeson, Robert O. 2 El Maroufy, Hamid 2 Fan, Kuangang 2 Fearnhead, Paul ...and 777 more Authors
all top 5

### Cited in 130 Serials

 97 Mathematical Biosciences 51 Journal of Mathematical Biology 37 Journal of Theoretical Biology 35 Journal of Applied Probability 33 Bulletin of Mathematical Biology 15 Advances in Applied Probability 15 Theoretical Population Biology 13 The Annals of Applied Probability 11 Statistics & Probability Letters 10 Stochastic Processes and their Applications 9 Applied Mathematics and Computation 9 Methodology and Computing in Applied Probability 7 Biometrics 7 Journal of Statistical Planning and Inference 6 Physica A 6 Computational Statistics and Data Analysis 6 Stochastic Models 5 Scandinavian Journal of Statistics 5 European Journal of Operational Research 5 Statistics and Computing 4 Electronic Journal of Probability 4 Mathematical Biosciences and Engineering 4 Journal of Biological Dynamics 3 Journal of Mathematical Analysis and Applications 3 The Annals of Statistics 3 SIAM Journal on Control and Optimization 3 Statistical Science 3 Random Structures & Algorithms 3 Computational Statistics 3 Communications in Statistics. Theory and Methods 3 Proceedings of the National Academy of Sciences of the United States of America 3 Bernoulli 3 Abstract and Applied Analysis 3 Chaos 3 Probability in the Engineering and Informational Sciences 3 Advances in Difference Equations 2 Computers & Mathematics with Applications 2 Journal of the Franklin Institute 2 Journal of Statistical Physics 2 The Annals of Probability 2 Probability Theory and Related Fields 2 Applied Mathematics Letters 2 Mathematical and Computer Modelling 2 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 2 Discrete and Continuous Dynamical Systems 2 Mathematical Problems in Engineering 2 European Series in Applied and Industrial Mathematics (ESAIM): Probability and Statistics 2 Journal of the Royal Statistical Society. Series B. Statistical Methodology 2 Journal of the Royal Statistical Society. Series C. Applied Statistics 2 Journal of Biological Systems 2 Discrete and Continuous Dynamical Systems. Series B 2 Internet Mathematics 2 Computational & Mathematical Methods in Medicine 1 Applicable Analysis 1 The Canadian Journal of Statistics 1 Discrete Applied Mathematics 1 Journal of Computational Physics 1 Mathematical Methods in the Applied Sciences 1 Physics Letters. A 1 Physics Reports 1 Chaos, Solitons and Fractals 1 Applied Mathematics and Optimization 1 Automatica 1 Biometrical Journal 1 Journal of Computational and Applied Mathematics 1 Journal of Computer and System Sciences 1 Journal of Multivariate Analysis 1 Kybernetika 1 Mathematics and Computers in Simulation 1 Ricerche di Matematica 1 Siberian Mathematical Journal 1 Statistica Neerlandica 1 Systems & Control Letters 1 Physica D 1 Acta Mathematicae Applicatae Sinica. English Series 1 International Journal of Approximate Reasoning 1 Asia-Pacific Journal of Operational Research 1 Journal of the Ramanujan Mathematical Society 1 European Journal of Applied Mathematics 1 Annals of Operations Research 1 Neural Computation 1 Differential Geometry and its Applications 1 Applied Mathematical Modelling 1 Journal of Statistical Computation and Simulation 1 Linear Algebra and its Applications 1 SIAM Journal on Applied Mathematics 1 Bulletin of the American Mathematical Society. New Series 1 Journal of Dynamics and Differential Equations 1 Test 1 Mathematical Methods of Statistics 1 The Electronic Journal of Combinatorics 1 Russian Journal of Numerical Analysis and Mathematical Modelling 1 Lifetime Data Analysis 1 Complexity 1 International Transactions in Operational Research 1 Mathematical Population Studies 1 Mathematical Methods of Operations Research 1 Journal of Applied Mathematics and Decision Sciences 1 Mathematical and Computer Modelling of Dynamical Systems 1 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences ...and 30 more Serials
all top 5

### Cited in 28 Fields

 423 Biology and other natural sciences (92-XX) 277 Probability theory and stochastic processes (60-XX) 98 Statistics (62-XX) 72 Combinatorics (05-XX) 41 Numerical analysis (65-XX) 38 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 31 Ordinary differential equations (34-XX) 29 Operations research, mathematical programming (90-XX) 18 Statistical mechanics, structure of matter (82-XX) 18 Systems theory; control (93-XX) 15 Dynamical systems and ergodic theory (37-XX) 11 Partial differential equations (35-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 9 Computer science (68-XX) 6 Information and communication theory, circuits (94-XX) 3 Field theory and polynomials (12-XX) 3 Linear and multilinear algebra; matrix theory (15-XX) 2 Special functions (33-XX) 2 Integral equations (45-XX) 2 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Topological groups, Lie groups (22-XX) 1 Real functions (26-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)