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Veliov, V., & Widder, A. (2016). Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity (No. 2016–03). http://hdl.handle.net/20.500.12708/39084
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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Report No.:
2016-03
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Date (published):
2016
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Number of Pages:
24
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Abstract:
The paper presents a model for the evolution of an infectious disease
in a population with individual-specific immunity. The immune
state of an individual varies with time according to its own dynamics,
depending on whether the individual is infected or not. The model
involves a system of size-structured (first-order) PDEs that capture
both the dynamics of the immune states and the transition...
The paper presents a model for the evolution of an infectious disease
in a population with individual-specific immunity. The immune
state of an individual varies with time according to its own dynamics,
depending on whether the individual is infected or not. The model
involves a system of size-structured (first-order) PDEs that capture
both the dynamics of the immune states and the transition between
compartments consisting of infected, susceptible, etc. individuals.
Due to the unavailability of precise data about the immune states
of the individuals, the main focus in the paper is on developing
a technique for set-membership estimations of aggregated quantities
of interest. The technique involves solving specific optimization
problems for the underlying PDE system and is developed up to a
numerical method. Results of numerical simulations are presented
for a benchmark model of SIS-type, potentially applicable to diseases
like influenza and to various sexually transmitted diseases.
