**3** Publications

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J Math Biol 2017 04 7;74(5):1081-1106. Epub 2016 Sep 7.

ORCOS, Institute of Statistics and Mathematical Methods in Economics, Vienna University of Technology, Wiedner Hauptstraße 8/E105-4, 1040, Vienna, Austria.

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.

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http://dx.doi.org/10.1007/s00285-016-1050-0 | DOI Listing |

http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5388773 | PMC |

April 2017

J Math Biol 2005 Aug 13;51(2):123-43. Epub 2005 Jul 13.

Institute of Mathematical Methods on Economics, Vienna University of Technology, Argentinierstrasse 8/119, 1040, Vienna, Austria.

The paper investigates a class of SIS models of the evolution of an infectious disease in a heterogeneous population. The heterogeneity reflects individual differences in the susceptibility or in the contact rates and leads to a distributed parameter system, requiring therefore, distributed initial data, which are often not available. It is shown that there exists a corresponding homogeneous (ODE) population model that gives the same aggregated results as the distributed one, at least in the expansion phase of the disease. However, this ODE model involves a nonlinear "prevalence-to-incidence" function which is not constructively defined. Based on several established properties of this function, a simple class of approximating function is proposed, depending on three free parameters that could be estimated from scarce data. How the behaviour of a population depends on the level of heterogeneity (all other parameters kept equal) - this is the second issue studied in the paper. It turns out that both for the short run and for the long run behaviour there exist threshold values, such that more heterogeneity is advantageous for the population if and only if the initial (weighted) prevalence is above the threshold.

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http://dx.doi.org/10.1007/s00285-004-0288-0 | DOI Listing |

August 2005

Theor Popul Biol 2004 Jun;65(4):373-87

Institute for Econometrics, Operations Research and Systems Theory, Vienna University of Technology, Argentinierstrasse 8/119, A-1040 Vienna, Austria.

This paper brings both intertemporal and age-dependent features to a theory of population policy at the macro-level. A Lotka-type renewal model of population dynamics is combined with a Solow/Ramsey economy. We consider a social planner who maximizes an aggregate intertemporal utility function which depends on per capita consumption. As control policies we consider migration and saving rate (both age-dependent). By using a new maximum principle for age-structured control systems we derive meaningful results for the optimal migration and saving rate in an aging population. The model used in the numerical calculations is calibrated for Austria.

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http://dx.doi.org/10.1016/j.tpb.2003.07.006 | DOI Listing |

June 2004

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