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DIFFERENTIAL EQUATIONS

Dst / sarc h I CHAIR IN MATHEMATICAL MODELS AND METHODS IN BIOENGINEERING AND BIOSCIENCES (M 3 B 2 ). RESEARCH SETTING, FOCUS & APPROACHES. MODELING. DIFFERENTIAL EQUATIONS. DYNAMICAL SYSTEMS . Variational Inequalities. Delay /INTEGRO DIFFERENTIAL EQUATIONS.

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DIFFERENTIAL EQUATIONS

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  1. Dst/sarchI CHAIR IN MATHEMATICAL MODELS AND METHODS IN BIOENGINEERING AND BIOSCIENCES (M3 B2)

  2. RESEARCH SETTING, FOCUS & APPROACHES MODELING • DIFFERENTIAL EQUATIONS • DYNAMICAL SYSTEMS • Variational Inequalities Delay/INTEGRO DIFFERENTIAL EQUATIONS • REACTION DIFFUSION EQUATIONS MODEL SOLUTION MODEL VALIDATION QUANTITATIVE-QUALITATIVE- DYNAMICS-COMPUTATIONAL ANALYSIS

  3. SELECTED RESEARCH QUESTIONS • Computational study of PDEs inverse problems and computer-based analysis of complex systems • Partial Differential Equations for modelling: • Cancer growth • Bacterial biofilms • Pattern formation • Transmission of queen honeybee pheromone • Trends in the mathematical modelling of the HIV/AIDS with impact on its control • Modelling the sterile insect technology against vector-borne diseases and fruit flies • Biomechanics of bone and fracture healing

  4. PRINCIPAL INVESTIGATORS R AnguelovA Bastos C ChimimbaM Chapwanya Dynamical systems Zoonotic diseases Biofilms H Brettschneider J Djoko Variational R Appadu Hyperbolic models A Yusuf S Garba Ecology of honeybees Epidemiology J Lubuma Numerical Analysis

  5. Some initiatives for development of human capital • Training a critical mass of local expertise • Research visiting programme • Regular scientific meetings • Recruiting Postdoctoral Fellows and postgraduate students • BSc & Honours degrees with majors in Mathematics & Biology • Career pathways for involved researchers • Under Twenty Mathematicians Programme

  6. COLLABORATIONS

  7. SELECTED EARLY OUTPUTS M Chapwanya, J Lubuma & R Mickens (2013): Nonstandard finite difference schemes for Michaelis–Menten type reaction-diffusion equations, 29, 337-360 R Anguelov, Y Dumont, J Lubuma & M Shillor (2014): Dynamically consistent nonstandard finite difference schemes for epidemiological models, 255, 161-182 4 Registered PhD students in 2013 1 Postdoc in 2013 1 Expected Postdoc in 2013 S Garba, M Safi & A Gumel (2013), Cross-immunity-induced backward bifurcation for a model of transmission dynamics of two strains of influenza,14 (2013), 1384-1403 R Anguelov, Y Dumont , J Lubuma & E Mureithi(2013): Stability analysis and dynamics preserving nonstandard finite difference schemes for a malaria model, 20, 101-122

  8. dankie • Thank you ke a leboga

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