Speaker
Description
In 1914 McKendrick came up with a method inspired by L. Boltzmann to describe the evolution of statistical distributions in an - in principle continuous - parameter space, also for the life sciences and the social sciences.This method leads to partial differential equations. Nevertheless, the Kermack-McKendrick models are often misinterpreted solely as the well-known SIR ODE-system for the dynamics of susceptibles, infectious and removed during an epidemic.
But McKendricks equations are by far more general. For instance the hydrodynamic limit of a stochastic epidemiological model, where two infection scenarios alternate, namely a) infections in separated groups of finite size; b) and infections at meeting places of finite capacity, where individuals meet randomly, also results in such a type of McKendrick system with polynomial infection force.
For this system of kinetic equations we derive invariants which uniquely determine the outcome of the model epidemics. Such kinetic equations allow to link global data of an epidemic with not so easily observable local rate dependencies.
Bibliography
@incollection {MR4772248,
AUTHOR = {Luckhaus, Stephan and Stevens, Angela},
TITLE = {A two level contagion process and its deterministic {M}c{K}endrick limit with relevance for the {C}ovid epidemic},
BOOKTITLE = {Probability and statistical mechanics---papers in honor of {E}rrico {P}resutti},
SERIES = {Ensaios Mat.},
VOLUME = {38},
PAGES = {343--358},
PUBLISHER = {Soc. Brasil. Mat., Rio de Janeiro},
YEAR = {2023},
ISBN = {978-85-8337-215-8; 978-85-8337-214-1},
MRCLASS = {60J76 (82C22 92D30)},
MRNUMBER = {4772248},
}
@incollection {MR4627973,
AUTHOR = {Luckhaus, Stephan and Stevens, Angela},
TITLE = {Kermack and {M}c{K}endrick models on a two-scale network and connections to the {B}oltzmann equations},
BOOKTITLE = {Mathematics going forward---collected mathematical brushstrokes},
SERIES = {Lecture Notes in Math.},
VOLUME = {2313},
PAGES = {417--427},
PUBLISHER = {Springer, Cham},
YEAR = {[2023] \copyright 2023},
ISBN = {978-3-031-12243-9; 978-3-031-12244-6},
MRCLASS = {35Q35 (45J05 92D30)},
MRNUMBER = {4627973},
DOI = {10.1007/978-3-031-12244-6_29},
URL = {https://doi.org/10.1007/978-3-031-12244-6_29},
}
@article {MR4550935,
AUTHOR = {Luckhaus, Stephan and Stevens, Angela},
TITLE = {A free boundary problem-in time-for the spread of {C}ovid-19},
JOURNAL = {J. Math. Biol.},
FJOURNAL = {Journal of Mathematical Biology},
VOLUME = {86},
YEAR = {2023},
NUMBER = {3},
PAGES = {Paper No. 45, 17},
ISSN = {0303-6812,1432-1416},
MRCLASS = {45K05 (92D30)},
MRNUMBER = {4550935},
MRREVIEWER = {Feiying\ Yang},
DOI = {10.1007/s00285-023-01881-0},
URL = {https://doi.org/10.1007/s00285-023-01881-0},
}
