Transmission dynamics of infectious diseases on transportation networks

Knipl Diána
Transmission dynamics of infectious diseases on transportation networks.
PhD, University of Szeged.

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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 (PhD)
Creators: Knipl Diána
Hungarian title label: Járványterjedés modellezése transzportációs hálózatokon
Title of the thesis in foreign language: Transmission dynamics of infectious diseases on transportation networks
Divisions: Doctoral School of Mathematics
Discipline label: természettudományok > matematika- és számítástudományok
Defence date label: 2014. September 19.
Item ID: 2200
Identification Number: 2817470
Date Deposited: 2014. May. 06. 14:19
Last Modified: 2015. Jun. 05. 09:18
Depository no.: B 5756
Supervisor label:
Supervisor Supervisor scientific name label
Dr. Röst Gergely
tudományos főmunkatárs, Ph.D., Szegedi Tudományegyetem
Reviewer label:
Reviewer name label Reviewer scientific name label
Dr Hartung FErenc
Dr Simon L. Péter
egyetemi tanár
egyetemi docens
President label:
President name label President scientific name label
Dr Hatvani László
Member label:
Member name label Member scientific name label
Dr. Kérchy László
Dr Móricz Ferenc
Dr Stachó László
egyetemi tanár
prof. emeritus
egyetemi tanár
Defence/Citable status: Defended.

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