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The maths behind the models

The maths behind the models

Mathematician Khalil Ezzinbi of Morocco wins the second TWAS-Hamdan Award for work that supports the modeling of populations great and small
Morrocan mathematician Ezzinbi Khalil is the winner of the 2022 TWAS-Mohammad A. Hamdan Award. [Photo provided]
Morrocan mathematician Khalil Ezzinbi is the winner of the 2022 TWAS-Mohammad A. Hamdan Award. [Photo provided]

Khalil Ezzinbi, a Moroccan mathematician who specializes in work important to reducing the complexity of systems analyzed by computer models, is the winner of the 2022 TWAS-Mohammad A. Hamdan Award.  

Ezzinbi is based at Cadi Ayyad University, Marrakech, Morocco. He was honoured for his contributions to the development of new methods for solving complex equations useful for systems modeling.

The award, named for the late TWAS Vice-President of the Arab Region, is given every two years. It recognizes outstanding mathematical work by a scientist living and working in Africa or the Arab Region, and comes with a US$5,000 prize.

Ezzinbi said he was grateful for the award, and added that it contributes to showing the importance of mathematics in Africa. “In Africa, we have a lot of talented students, but the problem is to push and guide them,” he said. “We need good supervisors, and then we need support, and then we can do a lot of great things in Africa.”

Making complex systems simpler

Ezzinbi's specialty is looking for ways to simplify partial functional differential equations. An active field of research for decades, these are equations in which a number’s sensitivity to change is measured in both the present and across the past. They are also too complex for computer models to use—unless they are simplified.

His work in particular feeds into the field of population dynamics, which uses differential equations to project how animals will develop in ecosystems. For example, population dynamics models can project changes in animal populations from information about how prey and predators behave. It also is useful for problems on the cellular scale—such as with rapidly growing cancer cells, or the spread of diseases such as COVID-19. 

And so, these equations are widely used in computer models for cell proliferation, epidemiology, evolution, ecology, molecular biology, tumor growth, cancer treatments, and other population dynamics problems. Ezzinbi's main work is to reduce the complexity of these equations, so that computer models can produce reliable results more efficiently. His research on them has been published in well-established journals including the Journal of Differential Equations, Proceedings of the American Mathematical Society and the Journal of Mathematical Analysis and Applications

Computer modelling, Ezzinbi pointed out, doesn’t require as many resources as a laboratory would. “You just have to solve your model and it gives you information about the future.”

How to support mathematics research in Africa

Ezzinbi said Africa is home to much talent capable of research-level mathematics. He has conducted multiple collaborations with early-career mathematicians in Africa, visiting their universities—in Algeria, Burkina Faso, Cameroon, Nigeria, Tunisia, and Senegal. He observed that these were some of their most promising PhD scholars in Mathematics. 

But, further programmes are needed to support the development of master’s and PhD-level mathematics research in Africa, Ezzinbi emphasized. Africa’s governments don’t have the resources to support the number of students who have the potential to develop such research skills. So, more scholarships are needed from wealthier countries. 

“For colleagues, they are very motivated to do research, but the issue is the financial support; they do not have enough such support to develop their research,” said Ezzinbi. “Africa has plenty of talented young students and researchers, we need to guide them and share with them the new ideas that we develop now around the world.”

Ezzinbi noted that talented students tend to prefer to study applied fields such as computer sciences and artificial intelligence. He wants to see more programmes that would facilitate the study of higher mathematics for university students, which would in turn support these other fields. 

“I propose to select the best and talented students and give them scholarships to study   mathematics,” he said. “We need to engage in discussions with students to explain the role of mathematics in our lives, because mathematics is everywhere. Even if we talk about artificial intelligence—behind that, there is a lot of mathematics.”

Sean Treacy