Prof R (Roumen) Anguelov

       
   
  Open Access version of Articles 
 

Tel: +2712 420-2874
Fax: +2712 420-3893
E-mail: roumen.anguelov@up.ac.za
Office: Botany Building 2-10

Position: Professor
Academic qualifications: MSc(Sofia), PhD(Unisa)
NRF rating: B3

Fields of interest: Modern philosophies, spiral dynamics

Research interests: Applications of Mathematics to population dynamics and epidemiology: zoonotic diseases, vector-borne infections, mosquito control, gene-drive into population, ecological systems. Mathematics motivated by biological applications: dynamical systems, PDEs, impulsive PDEs, interval analysis, validated numerics, nonstandard finite difference method, image analysis.                                                                               

Publications over the past five years:
Journal articles 
       
Anguelov R, Djoko JK, Lubuma JM-S Energy properties preserving schemes for Burgers' equation. Numerical Methods for Partial Differential Equations, 24(1)(2008), 41-59

Anguelov R, Kalenda OFK The convergence space of minimal usco mappings.   Czechoslovak Mathematical Journal 59(134)(2009), 101-128

Anguelov R, Rohwer CH LULU operators for functions of continuous argument. Quaestiones Mathematicae 32(2009), 187-202

Anguelov R, Lubuma JM-S, Minani F Total variation diminishing nonstandard finite difference schemes for conservation laws. Mathematical and Computer Modelling, 51(2010), 160-166

Anguelov, R, Lubuma JM-S, Minani F A monotone scheme for Hamilton-Jacobi equations via the nonstandard finite difference method. Mathematical Methods in the Applied Sciences 33(2010), 41-48

Anguelov R, Popova ED  Topological structure preserving numerical simulations of dynamical models.  Journal of Computational and Applied Mathematics, 235(2010), 358-365

Anguelov R, Fabris-Rotelli I  LULU Operators and discrete pulse transform for multidimensional arrays.  IEEE Transactions on Image Processing, 19(11), 3012-3023

Anguelov R, Lubuma JM-S, Shillor M  Topological dynamic consistency of non-standard finite difference schemes for dynamical systems.   Journal of Difference Equations and Applications, 17(12)(2011), 1769-1791

Anguelov R, Dumont, Y, Lubuma JM-S  Mathematical modeling of sterile insect technology for control of anopheles mosquito.  Computers and Mathematics with Applications, 64(2012), 374-389

Brettschneider H, Anguelov R, Chimimba CT, Bastos ADS  A mathematical epidemiological model of gram-negative Bartonella bacteria: does differential ectoparasite load fully explain the differences in infection prevalence of Rattus rattus and Rattus norvegicus?  Journal of Biological Dynamics, 6(2)(2012), 763-781

Anguelov R, Dumont Y, Lubuma JM-S, Mureithi EW  Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model.  Mathematical Population Studies, 20(2013), 101-122

Anguelov R, Dumont Y, Lubuma JM-S, M Shillor  Dynamically consistent nonstandard finite difference schemes for epidemiological models.  Journal of Computational and Applied Mathematics, 255(2014), 161-182

Anguelov R, Van der Walt JH  Algebraic and topological structure of some spaces of set-valued maps.  To appear in Computers and Mathematics with Applications

Conference proceedings

Anguelov R, Fabris-Rotelli I Discrete pulse transform of images. In: A Elmoataz, O Lezoray, F Nouboud and D Mammass (editors), Proceedings of the 3^rd International Conference on Image and Signal Processing, ICISP 2008, Springer-Verlag, Berlin Heidelberg 2008, Germany, pp 1-9, ISBN-10: 3-540-69904-X, ISBN-13: 978-3-540-69904-0

Anguelov R Dynamically consistent schemes for epidemiological models. In S Margenov, S Dimova and A Slavova (editors), 3^rd Annual Meeting of the Bulgarian Section of the Society for Industrial and Applied Mathematics (BGSIAM’08 Proceedings), Demetra Ltd, 2009, Sofia, Bulgaria, pp 11-14, ISSN: 1313-3357

Anguelov, R, Djoko JK, Lubuma, JM-S Numerical schemes that preserve properties of the solutions of the Burgers equation for small viscosity. In A Abdulle, J Banasiak, A Damlamain and M Sango (editors), Multiple Scales Problems in Biomathematics, Physics, Mechanics: and Numerics (Proceedings of CIMPA School 2007), Gakuto International Series in Mathematical Sciences and Applications 31(2009), pp 277-300

Anguelov R, Dumont Y, Lubuma JM-S, Shillor M Comparison of some standard and non-standard numerical methods for the MSEIR epidemiological model. In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp 1209-1212, ISBN: 978-0-7354-0708-4, ISSN: 0094-243X

Anguelov R, Dumont Y, Lubuma JM-S, Shillor M Dynamically consistent non-standard finite difference schemes for the MSEIR epidemiological model. In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp 1213-1216, ISBN: 978-0-7354-0708-4, ISSN: 0094-243X

Anguelov R, Popova E Reliable simulations for applied dynamical models. In TE Simons, G Psihoyios and Ch Tsitouras (editors), Proceedings of the International Conference on Numerical Analysis and Applied Mathematics, ICNAAM 2009, (Crete, Greece), American Institute of Physics Conference Proceedings 1168, 2009, USA, Vol 2, pp 1205-1209, ISBN: 978-0-7354-0708-4, ISSN: 0094-243X

Anguelov R, Kojouharov, H Continuous age-structured model for bovine tuberculosis in African buffalo. In MD Todorov and CI Christov (editors), Proceedings of the 1^st International Conference on Application of Mathematics in Technical and natural Sciences, (Sozopol, Bulgaria), American Institute of Physics Conference Proceedings 1168, 2009, pp 443-450, ISBN: 978-0-7354-0752-7

Anguelov R, Lubuma JM-S and Shillor M Dynamically consistent nonstandard finite difference schemes for continuous dynamical systems. In X Hou, X Lu, A Miranville, J Su and J Zhu (eds), Dynamical Systems and Differential Equations, Proceedings of the 7^th AIMS Conference, University of Texas at Arlington, Texas, USA), American Institute of Mathematical Sciences, 2009, pp 34-43, ISBN-10: 1-60133-011-1, ISSN-13: 978-1-60133-011-6

Anguelov R , Structurally stable numerical schemes for applied dynamical models. In I Lirkov, M Svetozar and J Wasniewski (Eds.), Proceedings of the 7^th International Conference on Large Scale Scientific Computing (LSSC), (Sozopol, Bulgaria), (Special volume of Lecture Notes in Computer Science, vol 5910), Springer 2010, pp 554-562, ISBN-10: 3-642-12534-4, ISBN-13: 978-3-642-12534-8

Anguelov R, Markov S, Minani F Hausdorff continuous viscosity solutions of Hamilton-Jacobi equations. In I Lirkov, M Svetozar and J Wasniewski (Eds.), Proceedings of the 7^th International Conference on Large Scale Scientific Computing (LSSC), (Sozopol, Bulgaria), (Special volume of Lecture Notes in Computer Science, vol 5910), Springer 2010, pp 231-238, ISBN-10: 3-642-12534-4, ISBN-13: 978-3-642-12534-8

Anguelov R, Brettschneider H, Bastos ADS  A case of multi-vector and multi-host epidemiology model: Bartonella infection.  In  MD Todorov and CI Christov (Eds.), Proceedings of the 2nd International on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’10), (Sozopol, Bulgaria), American Institute of Physics Conference Proceedings (AIP) 1301, 2010, pp 175-187, ISBN: 978-0-7354-0856-2

Anguelov R, Dumont Y, Lubuma JM-S, Mathematical modeling of sterile insect technology for control of Anopheles mosquito.  In CI Christov and MDTodorov (eds), Proceedings of the 3rd International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (Albena, Bulgaria), American Institute of Physics - AIP Conference Proceedings 1404, (2011), pp 155-161, ISBN: 978-0-7354-0976-7

Anguelov R, Plaskitt-Rotelli I  Locally monotone approximations of real functions ob graphs.  In G Nikolov and R Uluchev (eds), Proceedings of Constructive Theory of Functions, (Sozopol, Bulgaria), Marin Drinov Academic Publishing House (2012), pp 21-29, ISBN: 978-954-322-490-6

Anguelov R, Dumont Y, Lubuma JM-S  On non-standard finite difference schemes in Biosciences.  In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 212-223, ISBN: 978-0-7354-1099-2

Anguelov R, Fabris-Rotelli I  On the axiomatization of Scale-Space Theory.  In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 159-167, ISBN: 978-0-7354-1099-2

Anguelov R, Agbebaku D Van der Walt JH  Hausdorff continuous solutions of conservation laws.  In MD Todorov (editor), Proceedings of the 4th International Conference on Application of Mathematics in Technical and Natural Sciences (AMiTaNS’11), (St Constantine and Helena, Bulgaria), American Institute of Physics – AIP Conference Proceedings 1487, 2012, pp 151-158, ISBN: 978-0-7354-1099-2

Anguelov R, Lubuma JM-S  Mathematical Analysis of vector-borne diseases on plants.  In M Kang, Y Dumont and Y Guo (editors), 2012 IEEE 4th International Symposium on Plant Growth Modeling, Simulation, Visualization and Applications (PMA’12), (Shanghai, China), Institute of Electrical and Electronic Engineers (IEEE), Inc, 2012, pp 22-29, ISBN: 978-1-4673-0068-1