However, COVID-19 had spread out a long ago, but until now, the whole world is not getting rid of the disease. Every day the number is increasing throughout the world and of course, India is not an exception. At present India is at no 3 position based on the covid-19 cases. If we unable to control or predict the proper lockdown criteria, we may end up by top of the list soon. However, biological and medical research are going on, but Mathematical research is also not very lagging behind in this case. There is a powerful tool in Mathematics, namely, Mathematical Modelling that is working as a bridge between two extreme opposite subjects, Biology and Mathematics and give the opportunity for the researchers of both field to work together.
- What is the need of Mathematical Modelling in this scenario?
Biology and medical research is going on to invent medicine and vaccine for COVID-19. Then the common question may arise, “what is the need of Mathematics then?” Sometimes, it is not sufficient to get the idea of the biological system without understanding thoroughly between various parts of the system and Mathematical modelling exactly does that. Therefore, this works as a block diagram to the overall scenario.
Until now, we have no medicine or vaccine other that Lockdown. Now by analyzing the data of patients from various countries, a more suitable suggestion can be given for imposing the lockdown. Modelling comprises of Differential Equations, Statistics that help us to know about the stability of the situation. Therefore, for non-mathematics person, a brief idea is given about Mathematical Modelling.
- What is Mathematical Modelling
Using mathematical symbol and logic a real world phenomena can be represented mathematically, which is called the Mathematical Model for that. The process of constructing a mathematical model is called Mathematical Modelling.
After creating a mathematical Model, the model can be analyzed and the derived results can be justified with real world data. If the result match with real world biological data, then we may end up with a successful model. A schematic diagram can be more appropriate in this regard,
There are some limitations also of Mathematical Modelling. In earlier time, there were manual mode of data taking, which leads to data loss or unavailability of data. Due to that, justification of Models with real world data was sometimes failed. Now days each patient data is computerized in most cases and so availability of data is more and we can consider the data we want. Mathematical Models are more realistic for that reason.
Again, biological interactions within a body is very much nonlinear in nature. For representing these terms we got huge nonlinear terms which is not suitable for Mathematics. Some of the terms may be simplified using various mathematical software but most of the cases are very tough for calculations. In this regard, sometimes we use a simplification of nonlinearity by ignoring higher order terms or by linearizing those equations. By doing that, the nature of the original equations were changing which is not desirable.
Modelling is then also very much important to predict to the nature of a problem apart from its difficulties. For any branch of science formulation of situations are very important mathematically and it will give rise to a good research article. So basically, modelling is important thought branches of sciences and even in some other disciplines.
- Opportunities of research in Modelling on COVID 19
Many people often asked, “What is the direct applications of Mathematics in the real world?” The answer is COVID-19. Before COVID-19, many people were not aware of mathematical modelling and prediction. However, after this disease happens many researches are going on about the lifting of lockdown, namely unlock-1. Again, in many states including West Bengal, fresh lockdown is given to control the spreading of this disease. For this kind of decision, proper mathematical calculations will be there, which is coming from Mathematical Model. Now for various country, the nature of the same disease is different, so different models need to be implemented. Those models can be validated with data of that country only. For researchers in bio mathematics, this kind of disease is a golden opportunity for doing a fresh research. This unknown disease gives rise to many different aspects of symptoms every day which will enrich the research aspects of a researcher in bio mathematics. Till now no drug or vaccine is present. Once it will be discovered, the drug aspects can be incorporated in the mathematical model, which will make the model more realistic and help to predict the future upto some level.
If anybody want to do research in this field, he/she need to know the idea of differential equations and mathematical software like MATLAB, MATHEMATICA etc. This kind of research is very realistic now a days and interesting.
Readers are requested to understand that Mathematical modelling is not capable of invent any drug or vaccine and it will not be able to remove any disease from society. It is basically a block representation of a real life phenomena which will help researcher from other discipline to do their job easily.
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