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Dr. Ealasukanthan Thavanayagam

t ealasukanthan   Dr. Ealasukanthan Thavanayagam
BSc (Hons) (EUSL), MSc(UPDN), MSc(Greenwich, UK), PhD(Canterbury, NZ)
Senior Lecturer (Grade II)
Mobile: 076 6688 318



I am a senior lecturer in mathematics and I have taken up this permanent position following my PhD at the University of Canterbury, New Zealand. Before moving here, I had also engaged in further research in mathematical physiology as a visiting academic (research) at the University of Canterbury School of Mathematics and Statistics. I completed my honours degree here at the Eastern University, and obtained double master degrees; one from the University of Greenwich, the Great Britain, in Applied Mathematical Modelling and Scientific Computing (with Distinction) and the other one from the University of Peradeniya, in Industrial Mathematics. I am in my early research career, but have a great interdisciplinary research questions and interests which interplay between applied mathematics through life sciences, such as biology and medicine, and engineering. I also have research interests in mathematical modelling of soil-plant-atmospheric continuum as well as approximate first integrals and conservation laws of perturbed differential equations. I have been on active research collaborations with experts in my field and expect to develop further research collaboration with scholars in near future. As my research recognition, I had been invited to give invited-talk in international conference and workshops held in India and Britain. Apart from my research, I have number of years of experience in undergraduate teaching, gained here at the Eastern University and the University of Canterbury, New Zealand. I pride myself on my teaching and research professionalism.

Outside academia, I enjoy variety of food (but a light eater) and drive of nature-infinity. Whenever I feel free of professional imprisonment, I spend literally a very little spare time to read ancient Tamil history and literature as well as write poems in Tamil.


Journal Publications

  1. Ealasukanthan Thavanayagam, David J N Wall, Micro-Macro Communication Protocol and Spatial Patterning of Arterial Vasomotion, Mathematical Models and Methods in Applied Sciences, 2018 - under review (Journal I.F: 2.86)
  2. Ealasukanthan Thavanayagam, David J N Wall, “Modelling of Spatial Dynamical Silence in the Macroscopic Arterial-Domain”, SIAM Journal on Applied Dynamical Systems, 2018 (Journal I.F: 1.48). DOI:

Conference Proceeding

  1. T. Ealasukanthan, A. G. Johnpillai, “Integration of Nonlinear Differential Equations using Lie Point Symmetries”, 5th Annual Research Session, EUSL, Sri Lanka, 2006, p 42-50

Papers in draft form

  1. Ealasukanthan Thavanayagam, Andrew G Johnpillai, “Further Existence of Approximate First-Integrals and Approximate Group-Invariant Solutions for Ordinary Differential Equations”
    Target journal: SIAM Journal on Mathematical Analysis
  2. Ealasukanthan Thavanayagam, Choi-Hong Lai, “On the Numerical Study of Time-Dependent Urinary Excretion Rate of Metabolite”
    Target journal: Journal of Pharmacokinetics and Pharmacodynamics

Research Interest

My primary research interest is the interdisciplinary applied mathematical modelling. I apply different techniques from applied mathematics to model problems arising from agriculture, biology, engineering and medicine. At present, I am interested in the following research themes:

  • Biology: Mathematical modelling of human arterial cellular signalling
  • Medicine: Disease modelling and drug pharmacokinetics
  • Agriculture: Modelling of soil moisture content and plant-soil interaction
  • Applied Mathematics: Approximate integrals of perturbed ODEs
  • Engineering: Metal injection moulding (feedback & solvent debinding)

My recent projects for full time research positions are set out as below. Students who are interested in pursuing research in mathematical modelling are welcome and encouraged to contact me for an informal discussion. Interest in biology and/or medicine is desirable.

Project 1 (Biology): Modelling of Signalling between Smooth Muscle and Endothelial Cells in Human Artery

Arterial cellular communication between smooth muscle cells (SMCs) and endothelial cells (ECs) plays a role in cellular physiology and sometimes in pathophysiology. In the latter case, as one of the examples, it has been recently proposed that reversing endothelial dysfunction in atherosusceptible sites and lowering lipoproteins as earlier as safe are the combined therapies to prevent from the arterial plaque formation (atherosclerosis) which leads to arterial diseases such as myocardial infarction (heart-attack), stroke and thrombosis. To address such pathophysiological scenarios it is necessary to study the dynamics of cellular signalling in a healthy artery.

This project will be firstly focusing on studying the dynamics of cellular membrane potential in an arterial ring of discretely coupled small number of SMCs and ECs using our models developed so far. Secondly, it is aimed to study the spatiotemporal cellular dynamics of a heterocellular system (SMC-EC) using our reaction-diffusion system and results obtained in the discrete case. As special case, the heterocellular system constrained by physiological and pathophysiological scenarios will also be considered. Furthermore, our models will be coupled with Ca2+ models, and results from the study will be validated against the existing in- vitro, in-vivo or in-silico experimental results.

Project 2 (Medicine): Modelling of Glucose Homeostasis and Drug Pharmacokinetics for Betterments of Diabetes Patients

It has been reported by international diabetes federation that approximately 8.3% of the world population has diabetes, and this number is expected to rise to 9.9% by 2030. Therefore, the importance of studying and understanding the pathogenesis of this chronic and complex multifactorial disease is paramount to clinically treat patients. Mathematical modelling of glucose homeostasis together with insulin pharmacokinetics will give an avenue to propose new therapeutic method to clinically treat diabetes patients.

From the above point of view, this project is designed to include prospective pathways of glucose homeostasis proposed by V Chelliah et al., and study the corresponding insulin pharmacokinetics by the way of mathematical modelling, to fill the gaps between clinical and nonclinical models of diabetes. Furthermore, as an extension of this study, more comprehensive multiscale models from sub-cellular to whole-body level will be developed to understand an integrated mechanistic view of the glucose homeostasis and insulin pharmacokinetics which could eventually lead to improve control and treatment methods for diabetes. This work will be carried out with the collaboration of experts from UK.

Project 3 (Agriculture): Modelling of Soil-Moisture Content and Plant-Soil Interactions

Conventional agriculture requires an optimised application of fertilizers to maximize the yield from the target crop, minimize the cost of damages and to carry out better management practices. However, since the possibility of determining the exact amount of fertilizer with precision is not obvious, the use of fertilizers has been in excess to achieve optimum economical gain, and hence over fertilization of nutrients such as nitrate and phosphate contaminates ground water and surface water. However, mathematical modelling of plant-soil interaction from a single root level to the whole plant and field levels may give an avenue for the best agriculture management practices to achieve optimum growth of the target crop whilst optimizing the usage of fertilizers with a minimum undesirable effect on the environment.

This project is primarily designed to study the soil moisture content by modifying and utilizing the N-layer-M-phase models (ordinary differential equations elaborating N number of soil horizons and M number of phases of precipitation and evaporation) developed by us, in relation to in-depth soil characteristics. These models will then be validated against sensor field data and compared with the APSIM (agricultural production system sIMulator) models for betterments. With an extension of discrete system of coupled ODEs to spatial models, we will study further the spatiotemporal patterning of soil moisture content at multiple scale levels, upscaling from a single soil block (microscopic) to field (macroscopic) using the theory of mathematical homogenization. At a later stage, these models will be coupled with the existing multiple scale plant nutritional models for better agricultural practices. This work will be undertaken with the collaboration of scientists from New Zealand and Great Britain.


100 Level course (Semester 2)

  • MT1242: Mathematical Modelling 1

400 Level Course (Semester 1)

  • MT 4044 Partial Differential Equations


  • 2012-2015: University of Canterbury Doctoral Scholarship.
  • 2013: MACFAST Travel Grant, India.
  • 2011: Mathematical Sciences Post Graduate Award, University of Greenwich, UK

Positions Held

  • 09/2018 – onwards: Senior Lecturer (Grade II), Department of Mathematics, Eastern University, Sri Lanka
  • 01/2017 – 12/2018: Visiting Academic, University of Canterbury, New Zealand
  • 03/2013 – 06/2015: Teaching Assistant, Civil and Natural Resources Engineering, University of Canterbury, New Zealand
  • 07/2012 – 10/2012, 02/2013 – 06/2013: Tutor, School of Mathematics and Statistics, University of Canterbury, New Zealand
  • 10/2011 – 03/2012, 09/2006 – 12/2009: Assistant Lecturer, Department of Mathematics, Eastern University, Sri Lanka
  • 11/2005 – 08/2006: Tutor, Department of Mathematics, Eastern University, Sri Lanka