TY  - JOUR
A1  - Gerlach, Moritz
A1  - Glück, Jochen
A1  - Kunze, Markus
T1  - Stability of transition semigroups and applications to parabolic equations
JF  - Transactions of the American Mathematical Society
N2  - This paper deals with the long-term behavior of positive operator semigroups on spaces of bounded functions and of signed measures, which have applications to parabolic equations with unbounded coefficients and to stochas-tic analysis. The main results are a Tauberian type theorem characterizing the convergence to equilibrium of strongly Feller semigroups and a generalization of a classical convergence theorem of Doob. None of these results requires any kind of time regularity of the semigroup.
KW  - Transition probabilities
KW  - strong Feller property
KW  - asymptotic
KW  - behavior
KW  - invariant measure
KW  - parabolic equations
Y1  - 2023
U6  - https://doi.org/10.1090/tran/8620
SN  - 0002-9947
SN  - 1088-6850
VL  - 376
IS  - 1
SP  - 153
EP  - 180
PB  - American Mathematical Soc.
CY  - Providence
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chain with restricted range
JF  - Communications in algebra
N2  - Let X be an infinite linearly ordered set and let Y be a nonempty subset of X. We calculate the relative rank of the semigroup OP(X,Y) of all orientation-preserving transformations on X with restricted range Y modulo the semigroup O(X,Y) of all order-preserving transformations on X with restricted range Y. For Y = X, we characterize the relative generating sets of minimal size.
KW  - Order-preserving transformations
KW  - orientation-preserving
KW  - transformations
KW  - relative rank
KW  - restricted range
KW  - transformation
KW  - semigroups on infinite chain
Y1  - 2022
U6  - https://doi.org/10.1080/00927872.2021.2000998
SN  - 0092-7872
SN  - 1532-4125
VL  - 50
IS  - 5
SP  - 2157
EP  - 2168
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Dimitrova, Ilinka
A1  - Koppitz, Jörg
T1  - On relative ranks of the semigroup of orientation-preserving transformations on infinite chains
JF  - Asian-European journal of mathematics
N2  - In this paper, we determine the relative rank of the semigroup OP(X) of all orientation-preserving transformations on infinite chains modulo the semigroup O(X) of all order-preserving transformations.
KW  - Transformation semigroups on infinite chains
KW  - order-preserving
KW  - transformations
KW  - orientation-preserving transformations
KW  - relative rank
Y1  - 2020
U6  - https://doi.org/10.1142/S1793557121501461
SN  - 1793-5571
SN  - 1793-7183
VL  - 14
IS  - 08
PB  - World Scientific
CY  - Singapore
ER  - 
TY  - JOUR
A1  - Kretzschmar, Mirjam E.
A1  - Ashby, Ben
A1  - Fearon, Elizabeth
A1  - Overton, Christopher E.
A1  - Panovska-Griffiths, Jasmina
A1  - Pellis, Lorenzo
A1  - Quaife, Matthew
A1  - Rozhnova, Ganna
A1  - Scarabel, Francesca
A1  - Stage, Helena B.
A1  - Swallow, Ben
A1  - Thompson, Robin N.
A1  - Tildesley, Michael J.
A1  - Villela, Daniel Campos
T1  - Challenges for modelling interventions for future pandemics
JF  - Epidemics
N2  - Mathematical modelling and statistical inference provide a framework to evaluate different non-pharmaceutical and pharmaceutical interventions for the control of epidemics that has been widely used during the COVID-19 pandemic. In this paper, lessons learned from this and previous epidemics are used to highlight the challenges for future pandemic control. We consider the availability and use of data, as well as the need for correct parameterisation and calibration for different model frameworks. We discuss challenges that arise in describing and distinguishing between different interventions, within different modelling structures, and allowing both within and between host dynamics. We also highlight challenges in modelling the health economic and political aspects of interventions. Given the diversity of these challenges, a broad variety of interdisciplinary expertise is needed to address them, combining mathematical knowledge with biological and social insights, and including health economics and communication skills. Addressing these challenges for the future requires strong cross disciplinary collaboration together with close communication between scientists and policy makers.
KW  - Mathematical models
KW  - Pandemics
KW  - Pharmaceutical interventions
KW  - Non-pharmaceutical interventions
KW  - Policy support
Y1  - 2022
U6  - https://doi.org/10.1016/j.epidem.2022.100546
SN  - 1755-4365
SN  - 1878-0067
VL  - 38
PB  - Elsevier
CY  - Amsterdam
ER  -