EPIDELAY Research Group

Delay differential equations and mathematical biology

Principal Investigator: Gergely Röst


Publications

2016

El-Morshedy H, Röst G, Ruiz-Herrera A
Global dynamics of delay recruitment models with maximized lifespan
Zeitschrift für Angewandte Mathematik und Physik, in press

Nah K, Röst G
Stability threshold for scalar linear periodic delay differential equations
Canadian Mathematical Bulletin, minor revision

Knipl D, Röst G
Spatially heterogeneous populations with mixed negative and positive local density dependence
Theoretical Population Biology, 109, 6-15, 2016

Dénes A, Röst G
Global stability for SIR and SIRS models with nonlinear incidence and removal terms via Dulac functions
Discrete and Continuous Dynamical Systems - B, in press, 2016

Wu X, Röst G, Zou X
Impact of spring bird migration on the range expansion of Ixodes scapularis tick population
Bulletin of Mathematical Biology, 78(1), 138-168, 2016

2015

Liu M, Liz E, Röst G
Endemic bubbles generated by delayed behavioral response - global stability and bifurcation switches in an SIS model
SIAM Journal on Applied Mathematics, 75(1), 75-91, 2015

Nakata Y, Röst G
Global analysis for spread of infectious diseases via transportation networks
Journal of Mathematical Biology, in press

P Carmona, D Franco, A Ruiz-Herrera, The impact of dispersal on two patch heterogeneous metapopulations, Mathematical Modelling of Natural Phenomena, in press

Dénes A, Röst G
Impact of excess mortality on the dynamics of diseases spread by ectoparasites
in: Proceedings of the AMMCS-2013 conference (Applied Mathematics, Modeling and Computational Science), Waterloo,  Canada. Springer 2014. pp. 1-6, in press

A Ruiz-Herrera, F Zanolin, Horseshoes in 3D equations with applications to Lotka Volterra systems, to appear in NoDEA Nonlinear Differential Equations and Applications.

Kiss IZ, Röst G, Vizi Zs
Generalization of pairwise models to non-Markovian epidemics on networks
Physical Review Letters  115:078701, 2015

Gourley S, Liu R, Röst G
Age-dependent intraspecific competition in pre-adult life stages and its effects on adult population dynamics
European Journal of Applied Mathematics, 27(1), 131-156, 2016

Knipl DH, Pilarczyk P, Röst G
Rich bifurcation structure in a two-patch vaccination model
SIAM Journal on Applied Dynamical Systems 14:(2), 980-1017, 2015

Barbarossa MV, Dénes A, Kiss G, Nakata Y, Röst G, Vizi Zs
Transmission dynamics and final epidemic size of Ebola Virus Disease outbreaks with varying interventions
PLOS ONE 10(7): e0131398 (2015)

Barbarossa MV, Röst G
Immuno-epidemiology of a population structured by immune status:
a mathematical study of waning immunity and immune system boosting
Journal of Mathematical Biology, 71(6), 1737-1770, 2015

Barbarossa MV, Röst G
Mathematical models for vaccination, waning immunity and immune system boosting: a general framework
In: Mondaini RP (szerk.) BIOMAT 2014, 185-205, Singapore: World Scientific, 2015.

2014

Faria T, Röst G
Persistence, Permanence and Global Stability for an n -Dimensional Nicholson System
Journal of Dynamics and Differential Equations, 26(3), 723-744, 2014

K. Buddrus-Schiemann, M. Rieger, MV Barbarossa, A Hartmann et al.
Analysis of N-acylhomoserine lactone-dynamics in continuous cultures of Pseudomonas putida IsoF using ELISA and UHPLC/qTOF-MS-derived measurements and mathematical models
Analytical and Bioanalytical Chemistry, 406(25), pp. 6373 - 6383 (2014)

Knipl DH, Röst G
Large number of endemic equilibria for disease transmission models in patchy environment
Mathematical Biosciences, 258, 201-222,  2014

S Gourley, G Röst, HR Thieme
Uniform persistence in a model for bluetongue dynamics,
SIAM Journal on Mathematical Analysis, 46:(2) pp. 1160-1184. (2014)

E Liz, A Ruiz-Herrera
Global dynamics of discrete neural networks allowing non-monotonic activation functions
Nonlinearity, Vol. 27 (2014), 289-304.

Dénes A, Röst G
Global dynamics of a compartmental system modeling ectoparasite-borne diseases
Acta Sci. Math. (Szeged) 80:3-4(2014), 553-572

M. V. Barbarossa, K. P. Hadeler and C. Kuttler,
State-dependent neutral delay equations from population dynamics
Journal of Mathematical Biology, 69(4), pp 1027-1056 (2014)

T. Alarcon, Ph. Getto, Y. Nakata
Stability analysis of a renewal equation for cell population dynamics with quiescence
SIAM Journal on Applied Mathematics, 74, no. 4 (2014): 1266-1297

Nah K, Nakata Y, Röst G
Malaria dynamics with long incubation period in hosts
Computers and Mathematics With Applications, 68(9) 915-930, 2014

Y. Nakata, G. Röst
Global dynamics of a delay differential system of a two-patch SIS-model with transport-related infections
Mathematica Bohemica, in press

Röst G, Vizi Zs
Backward bifurcation for pulse vaccination
Nonlinear Analysis - Hybrid Systems, 94, 99-113, 2014

MV  Barbarossa, H.-O. Walther
Linearized stability for a new class of neutral equations with state-dependent delay
Differential Equations and Dynamical Systems, in press

Nah K, Röst G, Kim Y
Modelling Malaria Dynamics in Temperate Regions with Long Term Incubation Period
in: Mondaini RP (ed.) BIOMAT 2013 - Proc. International Symposium on Mathematical and Computational Biology, Toronto, Canada. World Scientific, 2014. pp. 263-285.

Pituk M, Röst G
Large Time Behavior of a Linear Delay Differential Equation with Asymptotically Small Coefficient
Boundary Value Problems, 2014:114

Y Enatsu, Y Nakata,
Stability and bifurcation analysis of epidemic models with saturated incidence rates: an application to a nonmonotone incidence rate.
Mathematical Biosciences and Engineering, 11(4),  785–805, 2014

G Röst
Baneling dynamics in the Legend of the Seeker, 249-264, Chapter 17 in
Mathematical Modelling of Zombies (ed. Robert Smith?), University of Ottawa Press

M Mohr, MV Barbarossa, C Kuttler,
Age-structured populations, delay equations and predator-prey interactions,
Math. Mod. Nat. Phen., 9(1), 92-107, 2014

E Liz, A Ruiz-Herrera,
Addendum to "Attractivity, multistability, and bifurcation in delayed Hopfield's model with non-monotonic feedback'' [J. Differential Equations 255 (11) (2013) 4244–4262
Journal of Differential Equations 257 (2014), 1307–1309

Dénes A, Röst G
Global dynamics for the spread of ectoparasite-borne diseases
Nonlinear Analysis - Real World Applications 18: pp. 100-107. (2014)

2013

DH Knipl, G Röst, J Wu,
Epidemic spread and variation of peak times in connected regions due to travel related infections - dynamics of an anti-gravity type delay differential model
SIAM J. Applied Dynamical Systems, 12(4), 1722–1762. (2013)

DH Knipl, G Röst,
Backward bifurcation in SIVS model with immigration of non-infectives,
Biomath 2:(2) Paper 1312051. 14 p. (2013)

Ph Getto, A Marciniak-Czochra, Y Nakata, MdM Vivanco
Global dynamics of two-compartment models for cell production systems with regulatory mechanisms,
Mathematical Biosciences, 245 (2) pp. 258-268 (2013)

Liz, G Röst
Global dynamics in a commodity market model
Journal of Mathematical Analysis and Applications, 398(2), pp 707–714, 2013

Y Ma, M Liu, Q Hou, J Zhao
Modelling Seasonal HFMD with the recessive infection in Shandong, China
Mathematical Biosciences and Engineering, 10(4), pp 1159-1171, 2013

A Dénes, P Kevei, H Nishiura, G Röst
On the risk of measles outbreaks in Europe after Euro 2012
International Journal of Stochastic Analysis,  Article ID 576381, 9 pages, Vol 2013

M Liu, G Röst, G Vas
SIS model on homogeneous networks with threshold type delayed contact reduction
Computers and Mathematics with Applications 66 (2013) 1534-1546

Y Nakata,
交通網を通して広がる感染症を記述した遅延微分方程  式モデル
Newsletter of the Japanese Society for Mathematical Biology, 70, 18-21, 2013

DH Knipl
Fundamental properties of differential equations with dynamically defined delayed feedback,
E. J. Qualitative Theory of Diff. Equ., No. 17 (2013), pp 1-18

2012


A Dénes, G Röst
Structure of the global attractors in a model for ectoparasite borne diseases
BIOMATH
1:(1) Article ID: 1209256 (2012)

BN Kim, K Nah, C Chu, SU Ryu, YH Kang, Y Kim
Optimal control strategy of Plasmodium vivax malaria transmission in Korea
Osong Public Health Res Perspect, 3(3), pp 128–136, 2012

DH Knipl, G Röst
Multiregional SIR model with infection during transportation
BIOMATH 1:(1) Article ID: 1209255 (2012)

Y Muroya, Y Enatsu, Y Nakata
Complete global dynamics of a delayed viral infection model with lytic and nonlytic effectors
SeMA Journal, vol 60, pp 27-50, 2012

M Liu, G Röst
Dynamics of an SIS model on homogeneous networks with delayed reduction of contact numbers
BIOMATH 1:(2) Article ID: 1210045, 2012

DA Jones, HL Smith, HR Thieme, G Röst
Spread of phage infection of bacteria in a Petri dish
SIAM J Appl Math, 72(2), 670-688, 2012

G Röst, Sh-Y Huang, L Székely 
On a SEIR epidemic model with delay
Dynamic Systems and Applications, 21, 33-48, 2012

G Röst
Global convergence and uniform bounds of fluctuating prices in a single commodity market model of Bélair and Mackey
E. J. Qualitative Theory of Diff. Equ., No. 26 (2012), pp. 1-9.

2011


DH Knipl, A Hulman (additional contribution: J Karsai, G Röst)
Dynamic Model of Pandemic Influenza with Age Structure and Vaccination
http://demonstrations.wolfram.com/DynamicModelOfPandemicInfluenzaWithAgeStructureAndVaccinatio/
 Wolfram Demonstrations Project, Published: October 8, 2011

DH Knipl, G Röst
Influenza modelling with Mathematica, in: Karsai J, Vajda R (eds.)
Interesting Mathematical Problems in Sciences and Everyday Life. Szeged - Novi Sad 2011.
pp 1-24. (ISBN:978-963-306-109-1)

DH Knipl,  G Röst 
Modelling the strategies for age specific vaccination scheduling during influenza pandemic outbreaks, Math Biosci Eng 8(1),  123-139 (2011)

G Röst
On an approximate method for the delay logistic equation,
Commun Nonlinear Sci Numer Simul 16(9), 3470-3474 (2011)

G Röst
SEI model with varying infectivity and mortality, in: Siddiqi AH, Singh RC , Manchanda P (eds.)
MATHEMATICS IN SCIENCE AND TECHNOLOGY: Mathematical Methods, Models and Algorithms in Science and Technology, Proc. Sat. Conf. of ICM 2010. New Delhi, India, 2010
World Scientific, Singapore, pp. 489-498  (ISBN:978-981-4338-81-3) 

Some previous publications of team members


K Nah, Y Kim and JM Lee
The dilution effect of the domestic animal population on the transmission of P.vivax malaria 
Journal of Theoretical Biology, 266,  299-306 (2010)

SM Moghadas,  CS Bowman, G Röst, DN Fisman and J Wu
Post-exposure prophylaxis during pandemic outbreak, BMC Medicine 7:73, 2009

M Liu, Zh Jin, M Haque
An impulsive predator-prey model with communicable disease in the prey species only,
Nonlinear Anal RWA 10(5), 3098-3111 (2009)

E Liz, G Röst
Dichotomy results for delay differential equations with negative Schwarzian derivative,
Nonlinear Anal RWA, 11(3), 1422-1430  (2010)

A Dénes, L Hatvani, LL Stachó:
Eventual stability properties in a non-autonomous model of population dynamics,
Nonlinear Analysis 73, 650-659 (2010)
 

University of Szeged, Bolyai Institute, European Research Council, Gergely Röst