Research Interests ( Find more details on Google Scholar or Scopus or MathSciNet)

Don't bother me, I am busy, proving and calculating

uh-oh, I am stuck, and I think I need a cofee or beer to get through

Differential equations (PDEs, ODEs and FDEs), difference equations, applied dynamical systems, mathematical biology.

Why these ?

Things are changing in the real world, and differential equations are equations involing derivatives which are rates of changes. This is why differential equations are so important in understanding many changing phenomenons in nature, including those in biology, physics, and even economics and finance. And this is also why I am interested in DEs and their applications.

It is commonly agreed that much of the mathematics in the 20th century was driven by physiscs. Now it is also widely believed that much of the mathematics in this century will be driven by biology---there are so many biological questions that can not be answered merely by biologists. It is high time for applied mathematicians to get in.

Among my works on applications of DEs to biological problems are the following featured examples of problem driven nature:

Why so many un-mutated bacteria can survive antibiotics? Oh, it is due to the altruistic role of the mutated fellows.

There are many species of virus in the real world, but why some choose budding while the others choose lytic way to release from their host cells in their replications? Read this for an explanation.

A variety of maralia species are currently endemic in different regions around the world, but is it possible for two different species to be co-peristent in a single region? Yes.

Asian long horn beetle invaded Canada in middle 2000's, causing panic in the West of GTA. Would the cut-burn control strategy work to eradicate this invasive beetle? Read Analytically Solving the Beetle Problem, which received A Nugget from SIAM , and was selected to republish, as a SIGEST paper, in SIAM Reviews (SIAM Rev. 53(2011), 321-345).

Coming with the seasonal flu is a new flu for which there is no vaccine yet, would taking the seasonal flu vaccine be of any use/help in preventing the new flu? Well, it depends

Funding (I am grateful to all these programs/agents from which I have received funding):

NSERC Discovery (2016-2021): $40,000 x 5
MITAC Elite PDF funding (2012-2013): $35,000
Ontario Ministry of Natural Resources (2011-2014): $55,000
NSERC Discovery Accelerator Supplements (2010-2013): $40,000 x3
NSERC Discovery (2010-2016): $35,000 x 6
Ontario Ministry of Science, Technology and Industry (PREA, 2005-2010):$140,000
NSERC Discovery (2005-2010): $20,000 x 5
Fields Institute (with L. Wahl and G. Webb, 2005):$10,000
NSF (USA) (with L. Wahl and G. Webb, 2005): $7000
MITAC-NCE (2005--2008, 2008---2012): $91,000
University of Western Ontario (Start-up, 2004-2006): $15,000
AARMS, Fields Institute and CRM (with H. Brunner and X.-Q. Zhao, 2004): $26,000
Petro-Canada Young Innovator Award(2002-2004): $25,000
NSERC Discovery (2000-2005): $15,000x 5
MITAC-NCE Fund (with S. Campbell et al, 1999-2002): $194,000
CFI (with D. Pike et al, 1999): $75,000
Memorial University of Newfoundland (Start-up, 1999-2002):$25,000