Set-membership estimations for the evolution of infectious diseases in heterogeneous populations.
The paper presents an approach for set-membership estimation of the state of a heterogeneous population in which an infectious disease is spreading. The population state may consist of susceptible, infected, recovered, etc. groups, where the individuals are heterogeneous with respect to traits, relevant to the particular disease. Set-membership estimations in this context are reasonable, since only vague information about the distribution of the population along the space of heterogeneity is available in practice. The presented approach comprises adapted versions of methods which are known in estimation and control theory, and involve solving parametrized families of optimization problems. Since the models of disease spreading in heterogeneous populations involve distributed systems (with non-local dynamics and endogenous boundary conditions), these problems are non-standard. The paper develops the needed theoretical instruments and a solution scheme. SI and SIR models of epidemic diseases are considered as case studies and the results reveal qualitative properties that may be of interest.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., Block 8, 1113, Sofia, Bulgaria.
Tsvetomir
T
Tsachev
ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8/E105-4, 1040, Vienna, Austria.
Vladimir M
VM
Veliov
ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8/E105-4, 1040, Vienna, Austria. andreas.widder@tuwien.ac.at.
Andreas
A
Widder
D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D003710:Demography; D006801:Humans; D008954:Models, Biological
Epidemic models; Heterogeneous population models; SI, SIR disease models; Set-membership estimation; Uncertain distributed systems