The aim of this project is to develop and analyse infinite dimensional dynamical models for the transmission dynamics and propagation of infectious diseases. We use an integrated approach which spans from the abstract theory of functional differential equations to the practical problems of epidemiology, with serious implications to public health policy, prevention, control and mitigation strategies in cases such as the ongoing battle against the nascent H1N1 pandemic.
Delay differential equations are one of the most powerful mathematical modeling tools and they arise naturally in various applications from life sciences to engineering and physics, whenever temporal delays are important. In abstract terms, functional differential equations describe dynamical systems, when their evolution depends on the solution at prior times.
The central theme of this project is to forge strong links between the abstract theory of delay differential equations and practical aspects of epidemiology. Our research will combine competencies in different fields of mathematics and embrace theoretical issues as well as real life applications.
In particular, the theory of equations with state dependent delays is extremely challenging, and this field is at present on the verge of a breakthrough. Developing new theories in this area and connecting them to relevant applications would go far beyond the current research frontier of mathematical epidemiology and could open a new chapter in disease modeling.
Fields of science
- natural sciencesmathematicsapplied mathematicsdynamical systems
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations
- medical and health scienceshealth sciencespublic healthepidemiology
- natural sciencesmathematicsapplied mathematicsmathematical model
- medical and health scienceshealth sciencesinfectious diseasesRNA virusesinfluenza
Call for proposal
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