Models of infectious disease and their numerical solution
Ján Gašper
PhD thesis advisor:
Daniel Ševčovič
PhD thesis consultant:
Soňa Kilianová
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PhD thesis - Full text 
Abstract:
In this thesis, known compartmental epidemiological models and approaches to their numerical solutions will be analyzed. The first result of this thesis
will be a new epidemiological model that includes immunity boosting of a recovered individual encountering an infectious individual. The new model will be generalized
for an arbitrary immunity loss curve. The second result of this thesis will be spatially heterogeneous model with population diffusion modeled by a fractional
Laplacian. The numerical solutions of new models will be implemented and the results will be visually presented.
References
[1] M Ehrhardt, J Gašper, S Kilianová: SIR-based mathematical modeling of
infectious diseases with vaccination and waning immunity. Journal of
Computational Science 37, 101027.