In an extraordinary feat of academic and research brilliance, Nida Javaid, a dedicated biologist, triumphed in her Ph.D. thesis defense by discussing her research on antimicrobial resistance (AMR) on clinically relevant pathogens. 2 weeks after her defense, she was awarded the coveted title of being a Ph.D. doctor. By inculcating the disciplines of Math and Biology, Dr. Nida employed various statistical analyses along with well-thought-out genomic epidemiological approaches to classify and characterize the patterns of Antimicrobial Resistance in Pakistan.

In her thesis presentation, Dr. Nida highlighted the dangers of antimicrobial-resistant pathogens. Due to factors such as lack of surveillance systems, inadequate infection control practices in hospitals, overburdened healthcare systems, and most importantly, the lack of awareness, AMR has become a major public threat in Pakistan. Dr. Nida’s statistical models primarily focus on the patterns of AMR in Pakistan, explicitly examining clinically resistant strains of Streptococcus pneumoniae (S. pneumoniae). S. Pneumoniae is the bacteria behind pneumococcal infections, a lower respiratory tract disease affecting millions worldwide. When bacteria become resistant to the antimicrobials provided as an infection cure, antimicrobial resistance develops, and this causes the birth of ‘Superbugs’.

During her research, Dr.Nida realized the intensity of this prevalent problem and noticed that the burden of pneumonia infections is unevenly distributed. A staggering 50% of bacterial infections and associated fatalities are concentrated in just four countries, with Pakistan being among them. In 2012, a therapeutic revolution was introduced with the discovery of PCV-10, a vaccine targeting 10 serotypes of S.Pneumonia. However, until now, no study has examined the impact of this vaccine on these resistant pathogens. This is when Dr. Nida knew that she had to play her part in understanding and researching these disease patterns. Through her work, she brought the country closer to developing stronger therapeutics and surveillance systems.

What truly sets Dr. Nida’s approach apart is her multi-faceted, interdisciplinary approach. In her prior academic works as the first or second author, Dr. Nida delved into analogous mathematical models of AMR patterns in clinically relevant bacteria. For instance, in her published article titled "Trends in antimicrobial resistance amongst pathogens isolated from blood and cerebrospinal fluid cultures in Pakistan (2011-2015): A retrospective cross-sectional study," she extensively examined antimicrobial resistance patterns, specifically in E. coli strains.

Her passion for Mathematics and Biology drove her to take a varied approach to tackle the problem. Her research was conducted under the guidance of multiple esteemed professors, including Dr. Shaper Mirza, Dr. Sultan Sial, Dr. Safee Chaudhary, and Dr. Adnan Khan, representing both the Math and Life Sciences departments at SSE. Additionally, she received supervision from Dr. Imran Nisar from Aga Khan University in Karachi. Dr. Nida's Ph.D. research also sets up a propeller for further research in therapeutics as she looks at other structural proteins of S.Pneumoniae as a vaccine target.

The use of mathematical modeling in the fight against diseases and pandemics is not new. Scientists and mathematicians have used mathematical modeling to identify the cause of diseases and estimate their transmission rates. Since it helps calculate the transmission rate and the proportion of the population at risk of infection, this methodology becomes crucial for pandemic control. For the recent novel coronavirus (COVID-19) too, such models were created, which helped gauge its spread and hence aided authorities in making suitable decisions to prevent its spread.  
 
Mohsin Ali, a Ph.D. student at the department of Mathematics at LUMS, formulated deterministic models for his Ph.D. thesis, which was successfully defended on Friday, May 5th ,2023. The thesis was titled “Mathematical Modelling of Some Infectious Diseases” and was examined by a committee including members from both LUMS and otter institutions such as Ajman University in UAE and the University of the Punjab in Lahore. The defense was supervised by Dr. Adnan Khan, an associate professor of Mathematics at LUMS.  

Dr. Mohsin’s primary data source was the NCBI database, and the initial model investigated the effects of asymptomatic persons in spreading the disease, which was the main issue with this disease i.e., the inability to observe symptoms early enough, making containing the disease a big challenge. Ali calculated the basic reproduction number based on incidence data from the initial outbreak in Wuhan. This estimate aligned with others and was considered low during the initial stages of the pandemic due to fewer infected individuals. He then covered isolation and quarantine procedures, as well as the medication and treatment needed to control the illness, into his calculations. From this, he predicted the COVID-19 epidemic curve during the pandemic's initial stages in Pakistan in 2020.

By analyzing incidence statistics for the pre-and post-relaxation period of social distancing measures, he calculated the fundamental reproduction number, which helped predict the epidemic curve. In the absence of significant attempts to manage the epidemic, the curve would have peaked around mid-September 2020. It was also found that the disease severity and illness-related factors are both linked to age and co-morbidities such as heart diseases and hypertension.  

Interestingly, in his thesis, potential patients were divided into two main groups; a low-risk group of teens with high immunities and a high-risk group comprising the elderly. It was evident that changes in the relative number of these low- and high-risk susceptible groups significantly influenced the effect of disease and mortality. Further, to understand how co-infection can affect pneumonia transmission, Dr. Mohsin examined the relationship between influenza and pneumonia respiratory illnesses. His model also exhibited a backwardly diverging curve in the presence of co-infection, indicating that bringing the disease’s reproduction rate to zero might not be sufficient. However, it can depend on the first susceptible population.

Numerical simulations and models were also presented to corroborate the theoretical conclusions of the thesis. An essential factor, 'Ro', was defined as the basic reproduction number that determined the decay or increase in the curves of the disease. 
The importance of basic Mathematics is often overlooked and imagined to be restricted to examinations and classrooms. However, with the right arithmetic and modeling, it is even possible to understand disease dynamics and take steps to counter it! 
 

The Department of Mathematics at the Syed Babar Ali School of Science and Engineering has been recognized as an Emerging Regional Centre of Excellence by the European Mathematical Society (EMS).

Emerging Regional Centers of Excellence are official partners in the EMS's mission to create and nurture mathematical knowledge at the finest order, focusing on the training of mathematicians who can then foray into research, industry and education. backed by the Department of Mathematics' commitment to world class and societally relevant education in fundamental and applied mathematics, this is indeed a distinct honor for the Department, School and the University. 

Over the past years, under the vision and leadership of Department Chair, Dr. Imran Anwar, we've seen a vitalization of activity through Math Circles, The John Conway Spirited Seminar series, the mathematical extravaganza with CIMPA, the introduction of the maths honors program and the strengthening of graduate level research activity.

This announcement, backed by mathematicians of international eminence, energizes our commitment to mathematics education at the finest level, human resource training in the country and in the region, and a progressively international outlook that encourages mobility and exchange of ideas and individuals. 

Through this recognition, LUMS SBASSE and our Mathematics Department join the ranks of emerging centers in Vietnam, Malaysia, Indonesia, Benin, Morocco, Nigeria, and Senegal.

Many congratulations to mathematics at SBASSE, LUMS and to the future of mathematical creativity in Pakistan!

---Muhammad Sabieh Anwar

Many claim that math is the language of the universe; string the words with careful deliberation and you might end up with an almost poetic reconstruction of reality. To the contrary of most of our school level pedagogy, mathematics can be perplexingly enriched with visuals, a form of visual poetry. In a universe that binds us in three spatial dimensions, mathematics is the ultimate liberator that lets us imagine, quite tangibly, the possibilities of dimensions higher (and lower) than what we inhabit. Be it a daedal tesseract, or a complex reconstruction of the Mandelbrot set, mathematics has an innate power to inform our wildest imagination.

Fukaya category is one startling example of the many ways in which complex mathematics can be expressed through the study of surfaces and topology.

Dr. Haniya Azam is an Assistant Professor at the department of mathematics who is the first author of a paper which has been published in the Journal of Pure and Applied Algebra, one of the most well reputed journals of mathematics. Dr. Haniya’s paper tackles the complex topic of mathematical surfaces called Fukaya category, a mathematical concept whose applications spill over to other disciplines, such as in the famous string theory, by providing vital support for the mirror symmetry conjecture.

This research constructs the topological Fukaya category of a surface with genus greater than one, making this model intrinsic to the topology of the surface.

Pictured above: non-separating curves on a surface of genus two.

In their paper, Dr. Haniya and her team review the definition of Floer homology for unobstructed curves. Floer chain complex will be generated by intersection points, which requires the usual transversality condition on the pair of curves giving these intersection points. Defined in this naive manner, their chain complexes are not invariant under isotopy. For a given choice of disjoint representatives of two curves the intersection could be empty, whereas a little perturbation may give rise to intersection points.

Instead of using the area form of the surface, the researchers use an admissibility condition borrowed from Heegaard-Floer theory which ensures invariance under isotopy. The paper shows finiteness of the moduli space using purely topological means and compute the Grothendieck group of the topological Fukaya category.

You can read the complete paper below for a much deeper dive into Dr. Haniya’s work.

Reference
Haniya Azam, Christian Blanchet, Topological Fukaya categories of surfaces, Journal of Pure and Applied Algebra, Volume 226, Issue 6, 2022, 106941, ISSN 0022-4049.