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J Biol Dyn. 2016 Dec;10(1):457-76. doi: 10.1080/17513758.2016.1221474.
Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity.
Veliov VM1, Widder A1.
Author information
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 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.
KEYWORDS:
35F10; 49K20; 92D30; 93E10; Mathematical epidemiology; heterogeneous SIS-models; immune status; immunoepidemiology; set-membership estimations; size-structured systems
PMID: 27548025 DOI: 10.1080/17513758.2016.1221474
[PubMed - in process]
Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity.
Veliov VM1, Widder A1.
Author information
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 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.
KEYWORDS:
35F10; 49K20; 92D30; 93E10; Mathematical epidemiology; heterogeneous SIS-models; immune status; immunoepidemiology; set-membership estimations; size-structured systems
PMID: 27548025 DOI: 10.1080/17513758.2016.1221474
[PubMed - in process]