Istvan Kiss

Professor of Applied Mathematics (Mathematics)

Careers Tutor

E: I.Z.Kiss@sussex.ac.uk

T: +44 (0)1273 873021

# Selected publications

### Article

Ashton, Stephen, Scalas, Enrico, Georgiou, Nicos and Kiss, István Zoltán
(2018)
*The mathematics of human contact: developing a model for social interaction in school children.*
Acta Physica Polonica A.
ISSN 0587-4246
(Accepted)

Sherborne, Neil, Blyuss, Konstantin and Kiss, Istvan
(2018)
*Bursting endemic bubbles in an adaptive network.*
Physical Review E (PRE), 97 (4).
042306.
ISSN 2470-0045

Rost, G, Vizi, Z and Kiss, I Z
(2018)
*Pairwise approximation for SIR type network epidemics with non-Markovian recovery.*
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 474 (2210).
ISSN 1364-5021

Sherborne, Neil, Miller, Joel C, Blyuss, Konstantin B and Kiss, Istvan Z
(2018)
*Mean-field models for non-Markovian epidemics on networks.*
Journal of Mathematical Biology, 76 (3).
pp. 755-778.
ISSN 0303-6812

Tee, Philip, Wakeman, Ian, Parisis, George, Dawes, Jonathan and Kiss, István Z
(2017)
*Constraints and entropy in a model of network evolution.*
European Physical Journal B: Condensed Matter and Complex Systems, 90.
p. 226.
ISSN 1434-6028

Sherborne, N, Blyuss, K B and Kiss, I Z
(2016)
*Compact pairwise models for epidemics with multiple infectious stages on degree heterogeneous and clustered networks.*
Journal of Theoretical Biology, 407.
pp. 387-400.
ISSN 0022-5193

Ritchie, Martin, Berthouze, Luc and Kiss, Istvan Z
(2016)
*Generation and analysis of networks with a prescribed degree sequence and subgraph family: higher-order structure matters.*
Journal of Complex Networks, 5 (1).
pp. 1-31.
ISSN 2051-1310

Szabó-Solticzky, András, Berthouze, Luc, Kiss, Istvan Z and Simon, Péter L
(2016)
*Oscillating epidemics in a dynamic network model: stochastic and mean-field analysis.*
Journal of Mathematical Biology, 72 (5).
pp. 1153-1176.
ISSN 0303-6812

Ritchie, Martin, Berthouze, Luc and Kiss, Istvan Z
(2016)
*Beyond clustering: mean-field dynamics on networks
with arbitrary subgraph composition.*
Journal of Mathematical Biology, 72 (1).
pp. 255-281.
ISSN 0303-6812

Simon, Péter L and Kiss, Istvan Z
(2016)
*Super compact pairwise model for SIS epidemic on heterogeneous networks.*
Journal of Complex Networks, 4 (2).
pp. 187-200.
ISSN 2051-1310

Juher, David, Kiss, Istvan Z and Saldaña, Joan
(2015)
*Analysis of an epidemic model with awareness decay
on regular random networks.*
Journal of Theoretical Biology, 365.
pp. 457-468.
ISSN 0022-5193

Georgiou, Nicos, Kiss, Istvan Z and Scalas, Enrico
(2015)
*Solvable non-Markovian dynamic network.*
Physical Review E, 92 (4).
042801.
ISSN 1539-3755

Sherborne, N, Blyuss, K B and Kiss, I Z
(2015)
*Dynamics of multi-stage infections on networks.*
Bulletin of Mathematical Biology.
pp. 1-25.
ISSN 0092-8240

Kiss, Istvan Z, Röst, Gergely and Zsolt, Vizi
(2015)
*Generalization of pairwise models to non-Markovian
epidemics on networks.*
Physical Review Letters (PRL), 115 (7).
ISSN 0031-9007

Sharkey, K J, Kiss, I Z, Wilkinson, R R and Simon, P L
(2015)
*Exact equations for SIR epidemics on tree graphs.*
Bulletin of Mathematical Biology, 77 (4).
pp. 614-645.
ISSN 0092-8240

Kiss, Istvan Z, Morris, Charles G, Sélley, Fanni, Simon, Péter L and Wilkinson, Robert R
(2015)
*Exact deterministic representation of Markovian SIR epidemics on networks with and without loops.*
Journal of Mathematical Biology, 70 (3).
pp. 437-464.
ISSN 0303-6812

Sélley, Fanni, Besenyei, Ádám, Kiss, Istvan Z and Simon, Péter L
(2015)
*Dynamic control of modern, network-based epidemic models.*
SIAM Journal on Applied Dynamical Systems, 14 (1).
pp. 168-187.
ISSN 1536-0040

Rattana, P, Berthouze, L and Kiss, I Z
(2014)
*Impact of constrained rewiring on network structure and node dynamics.*
Physical Review E, 90 (5).
ISSN 1539-3755

Taylor, Timothy J and Kiss, Istvan Z
(2014)
*Interdependency and hierarchy of exact and approximate epidemic models on networks.*
Journal of Mathematical Biology, 69 (1).
pp. 183-211.
ISSN 0303-6812

Hartley, Caroline, Taylor, Timothy J, Kiss, Istvan Z, Farmer, Simon F and Berthouze, Luc
(2014)
*Identification of criticality in neuronal avalanches: II. A theoretical and empirical investigation of the Driven case.*
Journal of Mathematical Neuroscience, 4 (9).
pp. 1-42.
ISSN 2190-8567

Nagy, N, Kiss, I Z and Simon, P L
(2014)
*Approximate master equations for dynamical processes on graphs.*
Mathematical Modelling of Natural Phenomena, 9 (2).
pp. 43-57.
ISSN 0973-5348

Miller, J C and Kiss, I Z
(2014)
*Epidemic spread in networks: existing methods and current challenges.*
Mathematical Modelling of Natural Phenomena, 9 (2).
pp. 4-42.
ISSN 0973-5348

Ritchie, Martin, Berthouze, Luc, House, Thomas and Kiss, Istvan Z
(2014)
*Higher-order structure and epidemic dynamics in clustered networks.*
Journal of Theoretical Biology, 348.
pp. 21-32.
ISSN 0022-5193

Rattana, P, Miller, J C and Kiss, I Z
(2014)
*Pairwise and edge-based models of epidemic dynamics on correlated weighted networks.*
Mathematical Modelling of Natural Phenomena, 9 (2).
pp. 58-81.
ISSN 0973-5348

Taylor, Timothy J, Hartley, Caroline, Simon, Péter L, Kiss, Istvan Z and Berthouze, Luc
(2013)
*Identification of criticality in neuronal avalanches: I. A theoretical investigation of the non-driven case.*
Journal of Mathematical Neuroscience, 3 (5).
pp. 1-26.
ISSN 2190-8567

Rattana, Prapanporn, Blyuss, Konstantin B, Eames, Ken T D and Kiss, Istvan Z
(2013)
*A class of pairwisemodels for epidemic dynamics on weighted networks.*
Bulletin of Mathematical Biology, 75 (3).
pp. 466-490.
ISSN 0092-8240

Kiss, Istvan Z and Simon, Péter L
(2012)
*New moment closures based on a priori distributions with applications to epidemic dynamics.*
Bulletin of Mathematical Biology, 74 (7).
pp. 1501-1515.
ISSN 0092-8240

Kiss, Istvan Z, Berthouze, Luc, Taylor, Timothy and Simon, Péter L
(2012)
*Modelling approaches for simple dynamic networks and applications to disease transmission models.*
Proceedings A: Mathematical, Physical and Engineering Sciences, 468 (2141).
pp. 1332-1355.
ISSN 1471-2946

Taylor, Michael, Simon, Peter L, Green, Darren M, House, Thomas and Kiss, Istvan
(2012)
*From Markovian to pairwise epidemic models and the performance of moment closure approximations.*
Journal of Mathematical Biology, 64 (6).
pp. 1021-1042.
ISSN 1432-1416

Kiss, Istvan and Simon, Peter L
(2012)
*From exact stochastic to mean-field ODE models: a new approach to prove convergence results.*
IMA Journal of Applied Mathematics.
ISSN 0272-4960

Taylor, Michael, Taylor, Timothy J and Kiss, Istvan Z
(2012)
*Epidemic threshold and control in a dynamic network.*
Physical Review E, 85 (1).
016103-1-016103-6.
ISSN 1539-3755

Bátkai, András, Kiss, Istvan Z, Sikolya, Eszter and Simon, Péter L.
(2012)
*Differential equation approximations of stochastic network processes: an operator semigroup approach.*
Networks and Heterogeneous Media, 7 (1).
pp. 43-58.
ISSN 1556-1801

Kiss, Istvan, Dent, JE, Kao, RR, Snow, L and Arnold, M
(2011)
*The spread of highly pathogenic avian influenza virus via dynamic contacts between poultry premises in Great Britain.*
BMC Veterinary Research, 7 (59).
ISSN 1746-6148

Kiss, Istvan Z, Cassell, Jackie, Recker, Mario and Simon, Péter L
(2010)
*The impact of information transmission on epidemic outbreaks.*
Mathematical Biosciences, 225 (1).
pp. 1-10.
ISSN 0025-5564

Kiss, Istvan Z, Simon, Péter L and Kao, Rowland R
(2009)
*A contact-network-based formulation of a preferential mixing model.*
Bulletin of Mathematical Biology, 71 (4).
pp. 888-905.
ISSN 0092-8240

Yakob, Laith, Kiss, István Z and Bonsall, Michael B
(2008)
*A network approach to modeling population aggregation and genetic control of pest insects.*
Theoretical Population Biology, 74 (4).
pp. 324-331.
ISSN 0040-5809

Kiss, Istvan Z and Green, Darren M
(2008)
*Comment on ''Properties of highly clustered networks".*
Physical Review E, 78 (4).
ISSN 1539-3755

Dent, Jennifer E, Kao, Rowland R, Kiss, Istvan Z, Hyder, Kieran and Arnold, Mark
(2008)
*Contact structures in the poultry industry in Great Britain: Exploring transmission routes for a potential avian influenza virus epidemic.*
BMC Veterinary Research, 4 (27).
pp. 1-14.
ISSN 1746-6148

Kiss, Istvan Z, Green, Darren M and Kao, Rowland R
(2008)
*The effect of network mixing patterns on epidemic dynamics and the efficacy of disease contact tracing.*
Journal of the Royal Society Interface, 5 (24).
791 - 799.
ISSN 1742-5689

Green, Darren M, Kiss, István Z, Mitchell, Andrew P and Kao, Rowland R
(2008)
*Estimates for local and movement-based transmission of bovine tuberculosis in British cattle.*
Proceedings B: Biological Sciences, 275 (1638).
1001 - 1005.
ISSN 1471-2954

Green, Darren M, del Rio Vilas, Victor J, Birch, Colin P D, Johnson, Jethro, Kiss, Istvan Z, McCarthy, Noel D and Kao, Rowland R
(2007)
*Demographic risk factors for classical and atypical scrapie in Great Britain.*
Journal of General Virology, 88 (12).
3486 - 3492.
ISSN 0022-1317

Kao, Rowland R, Green, Darren M, Johnson, Jethro and Kiss, István Z
(2007)
*Disease dynamics over very different timescales: foot-and-mouth disease and scrapie on the network of livestock movements in the UK.*
Journal of the Royal Society of London Interface, 4 (16).
907 - 916.
ISSN 1742-5689

Green, Darren M, Kiss, Istvan Z and Kao, Rowland R
(2006)
*Parasite strain coexistence in a heterogeneous host population.*
Oikos, 115 (3).
495 - 503.
ISSN 0030-1299

Green, D M, Kiss, I Z and Kao, R R
(2006)
*Modelling the initial spread of foot-and-mouth disease through animal movements.*
Proceedings B: Biological Sciences, 273 (1602).
2729 - 2735.
ISSN 1471-2954

Kiss, István Z, Green, Darren M and Kao, Rowland R
(2006)
*The network of sheep movements within Great Britain: network properties and their implication for infectious disease spread.*
Journal of the Royal Society Interface, 3 (10).
pp. 669-677.
ISSN 1742-5689

Kiss, István Z, Green, Darren M and Kao, Rowland R
(2006)
*The effect of contact heterogeneity and multiple routes of transmission on final epidemic size.*
Mathematical Biosciences, 203 (1).
pp. 124-136.
ISSN 0025-5564

Kao, R R, Danon, L, Green, D M and Kiss, I Z
(2006)
*Demographic structure and pathogen dynamics on the network of livestock movements in Great Britain.*
Proceedings B: Biological Sciences, 273 (1597).
1999 - 2007.
ISSN 1471-2954

Green, Darren M, Kiss, István Z and Kao, Rowland R
(2006)
*Parameterisation of individual-based models: Comparison with deterministic mean-field models.*
Journal of Theoretical Biology, 239 (3).
289 - 297.
ISSN 0022-5193

Kiss, Istvan Z, Green, Darren M and Kao, Rowland R
(2006)
*Infectious disease control using contact tracing in random and scale-free networks.*
Journal of the Royal Society Interface, 3 (6).
pp. 55-62.
ISSN 1742-5689

Merkin, J H and Kiss, I Z
(2005)
*Dispersion curves in the diffusional instability of reaction fronts.*
Physical Review E, 72 (2).
ISSN 1539-3755

Kiss, Istvan Z, Green, Darren M and Kao, Rowland R
(2005)
*Disease contact tracing in random and clustered networks.*
Proceedings B: Biological Sciences, 272 (1570).
pp. 1407-1414.
ISSN 1471-2954

Zadražil, A, Kiss, I Z, D'Hernoncourt, J, Ševčíková, H, Merkin, J H and De Wit, A
(2005)
*Effects of constant electric fields on the buoyant stability of reaction fronts.*
Physical Review E, 71 (2).
ISSN 1539-3755

Kiss, I, Merkin, J H, Scott, S K and Simon, P L
(2004)
*Electric field effects on travelling waves in the Oregonator model for the Belousov-Zhabotinsky reaction.*
Quarterly Journal of Mechanics and Applied Mathematics, 57 (4).
pp. 467-494.
ISSN 0033-5614

Kiss, I Z, Merkin, J H and Neufeld, Z
(2004)
*Homogenization induced by chaotic mixing and diffusion in an oscillatory chemical reaction.*
Physical Review E, 70 (2).
ISSN 1063-651X

Zhou, Changsong, Kurths, Jürgen, Neufeld, Zoltán and Kiss, István Z
(2003)
*Noise-sustained coherent oscillation of excitable media in a chaotic flow.*
Physical Review Letters, 91 (15).
ISSN 0031-9007

Kiss, I Z, Merkin, J H and Neufeld, Z
(2003)
*Combustion initiation and extinction in a 2D chaotic flow.*
Physica D: Nonlinear Phenomena, 183 (3-4).
pp. 175-189.
ISSN 0167-2789

Kiss, I Z, Merkin, J H, Scott, S K, Simon, P L, Kalliadasis, S and Neufeld, Z
(2003)
*The structure of flame filaments in chaotic flows.*
Physica D: Nonlinear Phenomena, 176 (1-2).
pp. 67-81.
ISSN 0167-2789

Neufeld, Zoltán, Kiss, István Z, Zhou, Changsong and Kurths, Jürgen
(2003)
*Synchronization and oscillator death in oscillatory media with stirring.*
Physical Review Letters, 91 (8).
ISSN 0031-9007

Kiss, I Z, Merkin, J H, Scott, S K and Simon, P L
(2003)
*Travelling waves in the Oregonator model for the BZ reaction.*
Physical Chemistry Chemical Physics, 5 (24).
5448 - 5453.
ISSN 1463-9076

Simon, Peter L and Kiss, Istvan Z
*On bounding exact models of epidemic spread on networks.*
Discrete and Continuous Dynamical Systems - Series B, 23 (5).
pp. 2005-2020.
ISSN 1531-3492

### Book

Kiss, István, Miller, Joel C and Simon, Péter L
(2017)
*Mathematics of epidemics on networks: from exact to approximate models.*
Interdisciplinary applied Mathematics, 46
.
Springer International Publishing.
ISBN 9783319508047

### Book Section

Kiss, Istvàn, Berthouze, Luc, Miller, Joel C and Simon, Péter L
(2017)
*Mapping out emerging network structures in dynamic network models coupled with epidemics.*
In:
Masuda, Naoki and Holme, Petter (eds.)
Temporal network epidemiology.
Theoretical Biology
.
Springer, pp. 267-289.
ISBN 9789811052866

Barnard, Rosanna C, Kiss, Istvan Z, Farmer, Simon F and Berthouze, Luc
(2017)
*Clustered arrangement of inhibitory neurons can lead to oscillatory dynamics in a model of activity-dependent structural plasticity.*
In:
van Ooyen, Arjen and Butz-Ostendorf, Markus (eds.)
The rewiring brain: a computational approach to structural plasticity in the adult brain.
Oxford: Academic Press, pp. 123-154.
ISBN 9780128037843

### Conference Proceedings

Messager, Antoine, Parisis, George, Harper, Robert, Tee, Philip, Kiss, István Z and Berthouze, Luc
(2018)
*Network Events in a Large Commercial Network: What can we learn?*
Published in: NOMS 2018 - IEEE/IFIP AnNet.
(Accepted)

Overbury, Peter, Kiss, Istvan Z and Berthouze, Luc
(2016)
*A genetic algorithm-based approach to mapping the diversity of networks sharing a given degree distribution and global clustering.*
5th International Workshop on Complex Networks and their Applications, Milan, 30th November - 2nd December 2016.
Published in: Cherifi, Hocine, Gaito, Sabrina, Quattrociocchi, Walter and Sala, Alessandra, (eds.) Complex Networks & Their Applications V.
693 223-233.
Springer
ISBN 9783319509006