title: Modelling and estimation of infectious diseases in a population with heterogeneous dynamic immunity.
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.
  
  
  
  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.
authors.affiliation: a ORCOS , Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology , Vienna , Austria.
authors.forename: V M
authors.initials: VM
authors.lastname: Veliov
authors.affiliation: a ORCOS , Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology , Vienna , Austria.
authors.forename: A
authors.initials: A
authors.lastname: Widder
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000276:immunology; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological
keywords: 35F10; 49K20; 92D30; 93E10; Mathematical epidemiology; heterogeneous SIS-models; immune status; immunoepidemiology; set-membership estimations; size-structured systems