Transmission dynamics of infectious diseases on transportation networks

Knipl Diána
Transmission dynamics of infectious diseases on transportation networks.
[Thesis] (Unpublished)

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Abstract in foreign language

Delay differential equations have numerous applications in science and engineering. They arise from the mathematical modeling of time-dependent processes where the evolution of the system is not only determined by the present state of the process, but it also depends on certain past states. These equations are different from ordinary differential equations, as the derivative of the unknown function at any time is given by the values of the function at present and prior times. In most applications of delay equations, the delayed feedback function is given explicitly. In this Ph.D.~dissertation we propose various models from population dynamics and epidemiology, where the delay terms in the model equations arise as the solution of another dynamical system. The general form of initial value problems for nonautonomous functional differential equations with such dynamically defined delayed feedback function will also be considered in this work. We obtain the usual existence, uniqueness and continuous dependence result for the solution, and show some other, biologically relevant properties. The results derived for the general framework enable us to analyze the model equations coming from biological applications, and in particular, they also provide a powerful tool to investigate some questions of major public health concern, such as the spatial spread of infectious diseases.

Item Type: Thesis (Doktori értekezés)
Creators: Knipl Diána
Magyar cím: Járványterjedés modellezése transzportációs hálózatokon
Divisions: Doctoral School of Mathematics
Tudományterület / tudományág: Natural Sciences > Mathematics and Computer Sciences
Nyelv: English
Date: 2014. September 19.
Item ID: 2200
A mű MTMT azonosítója: 2817470
doi: https://doi.org/10.14232/phd.2200
Date Deposited: 2014. May. 06. 14:19
Last Modified: 2020. Apr. 02. 08:28
Depository no.: B 5756
URI: https://doktori.bibl.u-szeged.hu/id/eprint/2200
Defence/Citable status: Defended.

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