It all depends.

In the UK, so I assume the EU, you cannot patent a mathematical model.

You can, I think, in the USA.

If your work uses anything that can be identified as part of the patent claims of the previous models then you may need to talk to a patent lawyer.

If this mathematical model is not equivalent to known and used mathematical models I think you can I still patent it of course, while citing the previous work.

Wish you all best.

Hey all, in order to open the discussion, you'll need to be aware of a few basic principles: a) patentability conditions, b) freedom-to-operate & doctrine of equivalence and c) exceptions of patentability.

a) a patent can be granted when your 'technical' invention is 1° new, 2° inventive and 3° industrial applicable. This third condition is 'here' important here because when talking about algorithms and mathematical formulae, they should be implemented in a particular application, such as a device, an apparatus, a process, etc. More particularly it is not enough to explain only the theoretical background, then you can choose for a scientific publication.

b) be aware of these already patented models, and you'll have to determine their scope of protection. When they claimed broadly and you use these already claimed features (in valid patents, covering your geographical market), you can be attacked for infringement, when entering these markets! So, you'll have to check your freedom-to-operate (FTO) for vending your product, with or without your own patent. Moreover, you can also be accused based on the doctrine of equivalence, when not exactly the same features of the patented technologies of others, but applying the spirit of invention even with your own slight differences. When you solve the same problem in a small different way, applying the fundamentals of the patented technologies, you'll need their authorisation to commercialize, like a license. A profound patent study is required here.

c) some 'non-technical' issues are not patentable, or at least open for discussion. This is i.a. the case with computer implemented inventions (software). This is mentioned in art.52 EPC (European Patent Convention): https://www.epo.org/law-practice/legal-texts/html/epc/2016/e/ar52.html. More specifically, art. 52 (2) (a) en (c) are important here. In the US: https://www.uspto.gov/web/offices/pac/mpep/consolidated_laws.pdf, art. 35 U.S.C. 101 and 103 are important. However, it could give you the impression that patentability is easier, less exclusions, etc... Case law in US states that abstract ideas and just data can be patented. Here again, the condition of a specific applications is required.

To finish my small intervention , a practical approach in a patent database. One of the patent classes that be used to search for models is: https://worldwide.espacenet.com/classification#!/CPC=G05B17/00. An example of a granted patent in this field is https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=20190925&DB=EPODOC&locale=en_EP&CC=EP&NR=2556414B1&KC=B1&ND=4#. In order to select the granted patents (or thus those that are patentable by the EPO) you'll have to choose EPB in the field of the publication number and combining this with the CPC field: G05B17/low. Another very important Class is https://worldwide.espacenet.com/classification#!/CPC=G16C

Another example: https://worldwide.espacenet.com/publicationDetails/originalDocument?FT=D&date=19990811&DB=EPODOC&locale=&CC=EP&NR=0494110B1&KC=B1&ND=4#. When looking at the claims: claim 1 describes a process for the estimation of the physical parameters....using a computer. The classifications G06F17/50: https://worldwide.espacenet.com/classification#!/CPC=G06F17/50 (which is broader for multiple applications) and G06F19 can also be very useful to search. https://worldwide.espacenet.com/classification#!/CPC=G16B are related to ICT applications (bioinformatics).

So, to conclude: 1° try to find similar granted patents and have a look at the claims what they exactly claim, 2° detect patents that you can infringe and check their legal status (preferably with professional assistance) in the framework of your FTO. If you don't have FTO, your are blocked for your future steps, if FTO think about step 3, 3° ask for a patent professional to analyze your model in order to evaluate the novelty and inventive step, and the techncial application. When you solve the problem with a feature that is not obvious for a skilled person and you don't use the fundamentals of earlier valid patents, unless you can agree a cross-license or an agreement of use, patentability is on the floor. The best.

Thank you all for your replies.

Special thanks to you Nico Deconinck, for the detailed answer.

Even a minor modification is sufficient for a patent application. Drafting the patent application is done by a patent attorney who knows how to do it correctly.

Dear Mr Lando, I completely agree with your statement, but patenting small change means that you are only projected for these small changes while you'll need to take the basic technology in account in the framework of your FTO. Choosing for patenting is a strategic choise based on many more than just protecting your technology...

I fully agree.

yes, you can file for patent . if your work based on previous model and you improve any section then it can be patent that part of work.