Understanding Disease Dynamics Through Applied Mathematics
How would you explain your research to someone outside mathematics, and what drew you to mathematical biology and epidemic modelling?
My research uses mathematical models to understand disease dynamics and explore how this knowledge might support more effective responses to health problems. Mathematical modelling helps us interpret complex phenomena and investigate the factors that shape them. Disease remains a major social challenge, making its study an important area in which mathematics can contribute.
The successful application of mathematical models in epidemiological settings can support better resource allocation, reduce costs and improve efficiency. My work also seeks to understand disease patterns involving memory effects, where a system’s past influences its present behaviour. These findings may provide insights into vaccination strategies, including the relationship between vaccine efficacy, resource needs and production costs.
Fractional calculus is central to many of your studies. In simple terms, what can this approach reveal about disease dynamics that conventional models might miss?
Fractional-order mathematical models provide an alternative framework in which the present dynamics can depend on the previous history of the biological system. This allows us to investigate memory effects in disease progression.
A planned comparison between a fractional-order model and its corresponding integer-order model will examine the influence of these memory effects. The aim is to understand how taking a system’s history into account may change our interpretation of its behaviour.
“Fractional-order mathematical models provide an alternative framework in which the present dynamics can depend on the previous history of the biological system.”
How do you assess whether a mathematical model captures what happens in the real world? Could you share a finding that surprised you?
Mathematical modelling is a useful tool across biology, economics and physics. It brings mathematical ideas and methods to real-world problems, while requiring careful consideration of the purpose of a model and the questions it is intended to address.
One direction of my research aims to simulate patient-specific outcomes by considering individual genetic, neurological and environmental characteristics. By examining how variations in these factors affect system stability, the work seeks to explore how genetic mutations, neurotransmitter imbalances or environmental stressors may trigger disorders.
The longer-term aim is to generate insights that could inform personalised treatment strategies suited to an individual’s disease profile. This reflects my broader interest in using mathematical models to improve our understanding of complex health problems.
How have your international experiences and collaborations shaped your research approach and your work at Near East University?
My international experiences and collaborations have significantly broadened my research perspective and strengthened my approach to applied mathematics. Working with researchers and institutions in different countries has exposed me to diverse mathematical techniques, research cultures and interdisciplinary perspectives. These experiences have encouraged me to connect theoretical questions with real-world applications, particularly in mathematical modelling, fractional calculus, dynamical systems and mathematical biology.
Many of my projects involve researchers from different disciplines and countries. This has helped me develop collaborative approaches to complex problems in epidemiology, disease dynamics, control theory and computational mathematics. It has also strengthened the importance I place on open scientific communication, knowledge sharing and mentoring young researchers.
At Near East University, I try to bring this international outlook into my research and academic responsibilities. Through the Mathematics Research Center, I have worked to promote collaboration, research seminars, academic exchange and interdisciplinary research opportunities. I believe that an internationally connected research environment helps faculty and students engage with emerging mathematical methods while also addressing problems of global relevance.
“My international experiences and collaborations have significantly broadened my research perspective and strengthened my approach to applied mathematics.”
You were recognised at the 2026 NEU Science Awards. What does this recognition mean to you, and beyond publication and citation counts, how do you define meaningful research?
Being recognised at the 2026 Near East University Science Awards is deeply meaningful to me. I see it as an acknowledgement of the collective effort of my students, collaborators, colleagues, the Mathematics Research Center and Near East University. Their support has helped create an environment in which meaningful research can develop.
Publications and citations are important indicators of research activity and scientific visibility, but I do not believe they fully define its value. For me, meaningful research addresses a genuine problem, develops reliable and innovative methods, and has the potential to contribute beyond the academic paper itself.
In applied mathematics, this can mean developing models that help us understand complex biological, environmental, economic or social systems, or creating mathematical and computational tools that other researchers can build upon. I also consider the training of young researchers an important measure of meaningful research. When a research project inspires students, develops their scientific thinking, creates new collaborations, or opens the door to further discoveries, its impact extends far beyond its publication.
This recognition motivates me to continue combining mathematical theory with computation, interdisciplinary applications and international collaboration. It reinforces my belief that the purpose of research is to create knowledge that is useful, reproducible, shareable and capable of making a lasting contribution to science and society.
“When a research project inspires students, develops their scientific thinking, creates new collaborations, or opens the door to further discoveries, its impact extends far beyond its publication.”
Looking ahead, what research question are you most eager to explore, and what advice would you give young researchers seeking to develop their own original ideas?
I believe that scientific excellence carries with it a responsibility to contribute to the advancement of society. Throughout my career, a central concern has been how my work can benefit others and contribute to my institution and the wider community.
Alongside my teaching responsibilities, I aim to develop scientific knowledge and explore emerging research directions that can help address real-life problems. My future work will continue to connect mathematical knowledge and innovation with the challenges faced by society.
Building relationships, partnerships and collaborations with other institutions is an important part of this approach. Through multidisciplinary research, I hope to contribute to new scientific directions and develop work with meaningful and lasting impact.
“I believe that scientific excellence carries with it a responsibility to contribute to the advancement of society.”
About the Researcher
His research spans mathematical biology, numerical analysis, control theory, disease modelling and the application of fractional calculus to epidemiology. He has published more than 350 research papers in journals indexed in the Science Citation Index and Scopus, and has supervised more than 50 master’s students and six doctoral students. He serves as Editor-in-Chief of the Journal of Mathematical Modeling and Fractional Calculus and reviews for a range of international journals.
His collaborative research includes projects with Prince Sattam bin Abdulaziz University and Universitas Airlangga on long-term disease suppression, mathematical epidemiology, smoking dynamics, non-communicable diseases and the application of fractional-order models in health sciences. A recent research fellowship at Universitas Airlangga examined the modelling and stability of neurological disorders using a fractal-fractional approach, with support through Indonesia’s LPDP-funded EQUITY Programme.
Dr. Farman’s distinctions include research awards from the University of Lahore and Near East University, recognition in the World’s Top 2% Scientists list, and best paper awards at international conferences in 2025 and 2026. His work combines mathematical theory, computational methods and international collaboration, alongside teaching and the supervision of postgraduate researchers.