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Department of Mathematics and Applied Mathematics

 
  Prof R (Roumen) Anguelov

       
   
  Open Access version of Articles 

 




Tel: +2712 420-2874 / 2520 
Fax: +2712 420-3893
E-mail: roumen.anguelov@up.ac.za
Office: Mathematics 1-39.2

Position:
Professor and Head of Department
Inaugural address 

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, 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 norvegicusJournal 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, Van der Walt JH  Algebraic and topological structure of some spaces of set-valued maps.  Computers and Mathematics with Applications, 66(2013), 1643-1654

Dufourd C, Weldon V, Anguelov R, Dumont Y  Parameter identification in population models for insects using trap data, Biomath 2(2)(2013), Article ID 1312061, 10 pages

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

Anguelov R, Garba SM, Usaini S  Backward bifurication analysis of epidemic model with partial immunity.  To appear in
Computers and Mathematics with Applications

Conference proceedings

Anguelov R , Structurally stable numerical schemes for applied dynamical models. In I Lirkov, M Svetozar and J Wasniewski (Eds.), Proceedings of the 7th 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 7th 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, Dumont Y, 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