Which one is best in modeling deterministic model, stochastic model or fractional differential equation model?
It would be good to read some intro book on mathematical modeling. The subject is huge. It all started in physics and later shifted within all scientific disciplines.
Next, you just learn to define your model inputs. To formalize the observed natural phenomenon using some sort of mathematical formalism.
It is where your question aims. To learn this, I recommend reading many reviews on modeling that are close to your research area. It gives you insights. It gives you intuition. It enables you to write down formalized models.
The next natural step is to write down a computer model or use some library to implement your model into a computer form. A few models are solvable analytically.
Many people think that it is the moment when your research ends. Not so much. You will find out that the output of the model does not agree with the observed phenomenon. That means, you just go back to the beginning to find out what is missing and repeat the whole procedure.
Well since stochastic models are not deterministic I would go with fde. I would prefer to know what I was modeling before making a choice.
best, D. Booth
The selection of the model always depends upon the perspective of the study. If you want to study the randomness in the system you have ro choose sde over ode. Similarly, if you want to study the inherent delay in the biological processes, you have to go for delay differential equations.
You nay go through the following article for more insight
https://academic.oup.com/bib/advance-article/doi/10.1093/bib/bbaa286/5985288
It would be good to read some intro book on mathematical modeling. The subject is huge. It all started in physics and later shifted within all scientific disciplines.
Next, you just learn to define your model inputs. To formalize the observed natural phenomenon using some sort of mathematical formalism.
It is where your question aims. To learn this, I recommend reading many reviews on modeling that are close to your research area. It gives you insights. It gives you intuition. It enables you to write down formalized models.
The next natural step is to write down a computer model or use some library to implement your model into a computer form. A few models are solvable analytically.
Many people think that it is the moment when your research ends. Not so much. You will find out that the output of the model does not agree with the observed phenomenon. That means, you just go back to the beginning to find out what is missing and repeat the whole procedure.
I prefer a balanced vision for modelling.
I explained it in my book
Book Fundamental Constants: Evaluating measurement Uncertainty
Mathematical Modeling is dictated principally by the problem and objectives under study, hence the choice of the techniques and their performance is dependent on the nature of the problem itself, there are no good or bad modeling methods in absolute sense, but all provide varying depths and clarity of insights into the problem posed.
Hello to everybody.
It seems that, in one way or another, all the answers tell the same - that the question is very abstract and nobody can recommend anything because the problem has not been specified.
Hi!
I must say that depends on your research question. The same phenomena can be modelled with diverse formalisms (stochastic, deterministic, partial equations to consider particle movement, etc), and everyone will give you valuable information, but every formalism has limitations. For example, a gene expression model. If you want to know the regulation and you have information about the kinetic parameters, maybe the best choice is a deterministic model. If you want to evaluate the effect of thermal fluctuations in the interaction of the polymerase and the promoter region, maybe the best choice is a stochastic model.
Perhaps it has been already covered by contributors above but I hope you understand that your question sounds like asking "What is the best car out there to buy?".
Personally, in choosing a model, I first, decide between a deterministic and a stochastic one (do I really need to model uncertainty or I can afford to not do so?) and second, choose among a whole zoo of mathematical models the one I believe (based on as rigorous mathematical evidence as possible) better represents the problem in question. And remember, "all models are wrong; just some are useful", that means, no model is able to fully capture all variables/dependencies/uncertainties but some can do that (much) better than others and produce valuable or directly interpretable outputs. Some times, the question is not about "what model should I use?" but "what model should I, by all means, avoid using?".
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