Forschungsgruppe ORCOS
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Modeling and Control of Contagious Phenomena in Heterogeneous Populations

FWF-Project No. P24125-N13, 2012-2016, Project leader: V. Veliov

Keywords: contagious phenomena, heterogeneity,  distributed systems, optimization, control

 

The annual economic losses due to influenza in the USA are estimated at over $80 bn. The HIV/AIDS prevalence among 15-49 years old women in Botswana and Zimbabwe is above 25%. These two figures alone show the huge size of the humanitarian and economic consequences of communicable diseases, even not counting numerous other epidemic diseases in human or animal populations.Evidently, the development of new medical tools is of immense value, but the ability to predict the evolution of epidemic diseases and to compose efficient policies (educational and medical prevention, monitoring, treatment, etc.) is of crucial importance as well, and even modest improvements may have large impacts.

The present project aims to further develop the mathematical modeling and simulation tools and to facilitate the dynamic policy optimization in this area. The most important specific feature of the project is that its starting point of investigation are relevant dynamic models of heterogeneous populations. Heterogeneity (with respect to genetic factors, habits, behavioral hazard, age etc.) may play a substantial role in the evolution of communicable diseases. On the other hand, models of infectious diseases in heterogeneous populations that explicitly take into account the heterogeneity are not only hard for numerical processing but, more importantly, require distributed data that are often either unavailable or unreliable.

For this reason one of the two main goals of the study is to develop new aggregation techniques capable of implicitly taking into account the heterogeneity within models that need not be supplied with detailed distributed data and, on the other hand, have a much simpler analytic structure. This will allow a more realistic numerical simulation, hence prediction, of the evolution of infectious diseases and a more profound qualitative investigation. These techniques will also be applied to other social processes driven by contagious phenomena, such as illicit drug “epidemics”.

The second main goal of the project is to further develop and implement methods from optimal control theory for designing optimal prevention and treatment policies. Different “performance” criteria of humanities-related/demographic or economic nature will be involved. The novelty is again the explicit or implicit consideration of the population’s heterogeneity. Optimal control policies obtained by using explicit modeling of heterogeneous populations are hard to apply in reality due to lacking data or to technical reasons, while those obtained by using the aggregated models developed within the first goal mentioned above require less data and are easier to implement. The efficiency and the qualitative properties of the latter control policies will be compared with those of the former ones.

The proposed investigation will have the additional effect of promoting the application of the involved powerful mathematical tools, in particular those from optimal control theory, in the areas of epidemiology and health economics.

 

Publications based on the work on FWF Project P 24125-N13 till March, 2015

[1] A. Widder. Dealing with different types of population heterogeneity in epidemiological models.
Research Report 2013-03, ORCOS, TU Wien, 2013.

[2] M.-L. Schelander. Using agent-based-modeling to calibrate dynamical models of contagious diseases.  Master Thesis, ORCOS, TU Vienna, 2012. 

[3] M. Kallian. Nonlinear incidence functions in mathematical epidemiology. Master Thesis, ORCOS, TU Vienna, 2012.

[4] A.L. Dontchev, M. Krastanov, R.T. Rockafellar, and V.M. Veliov. An Euler-Newton continuation method for tracking solution trajectories of parametric variational inequalities.  SIAM J. Control Optim., 51(3):1823-1840, 2013.

[5] V.M. Veliov and A. Widder. Aggregation and asymptotic analysis of an SI-epidemic model for heterogeneous populations. Research Report 2014-04, ORCOS, TU Wien, 2014. (Submitted to a journal.)

[6] F.J.A. Artacho, A. Belyakov, A.L Dontchev, M. Lopez. Local convergence of quasi-Newton methods under metric regularity. Computational Optimization and Applications, Oct. 2013.

[7] I. Hollick. Thresholds in the optimal treatment of infected heterogeneous populations. Master Thesis, ORCOS, TU Vienna, 2013.

[8] G. Feichtinger, A. Prskawetz, A. Seidl, C. Simon, S. Wrzaczek: Do Egalitarian Societies Boost Fertility? Research Report 2013-05, ORCOS, TU Wien, 2013. Submitted.

[9] M. Quincampoix and V.M. Veliov. Metric regularity and stability of optimal control problems for linear systems. SIAM J. Contr. Optim. 51(5):4118-4137, 2013.

[10] A. Widder, C. Kuehn. Heterogeneous Population Dynamics and Scaling Laws near Epidemic Outbreaks. Research Report 2014-08, ORCOS, TU Wien, 2014.

[11] V.M. Veliov. Numerical Approximations in Optimal Control of a Class of Heterogeneous Systems. Research Report 2015-01, ORCOS, TU Wien, 2015.

[12] R.M. Kovacevic and A. Pichler. Tree Approximation for Discrete Time Stochastic Processes -- A Process Distance Approach. Research Report 2015-02, ORCOS, TU Wien, 2015.

[13] B. Skritek. On the Optimal Control of Heterogeneous System. PhD Thesis. Research Report 2015-07, ORCOS, TU Wien, 2015.

[14] R. Kovacevic. Stochastic SIS epidemic models – the PDE-approach. Research Report 2015-09, ORCOS, TU Wien, 2015.