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:
- Recent lab work has shown that AS1 bacteria can block the maralia protozoan in the vector mosquitoes, can we use the AS1 infected mosquitoes to control maralia in the real world? Read this for a partial answer
- 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.
- 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