*The limited success of National AIDS Control Programme (NACP) I and II set up in the 1990s meant that the government had to something different to control HIV spread: India had roughly one-eighth of the world’s HIV burden. And in 2002, the US National Intelligence Council projected that by 2010, about 20-25 million people will be living in India with HIV. So the Indian policymakers approached a mathematician, Arni SR Srinivasa Rao, who was earlier a fellow at IISc, to develop a model to shape prevention strategies, which was eventually incorporated in the NACP III.*

*Rao led this effort from the University of Oxford by collaborating with colleagues in India and the UK to build a mathematical model, and predicted that by achieving a 50% target with antiretroviral treatment along with prevention, care and support, the government could bring down the number of people living with HIV from 2.4 million in 2006 to 2.08 million in 2011. This prediction turned out to be close: in 2011, the infection burden was brought down to 2.089 million individuals.*

*In an email interview with* Connect, *Rao, who is now Associate Professor in the Medical College of Georgia, Augusta University, USA, spoke about his work and how he was drawn to mathematical modelling for disease control.*

**What drew you to the field of mathematical modelling of diseases?**

During high school and early college days in Vizianagaram in Andhra Pradesh, my teacher, M Perisastri who had published seminal works in number theory in the 1950s and 1960s that attracted researchers worldwide, inspired me a lot. His teachers were prominent Indian mathematicians at Andhra University, such as T Vijayaraghavan, V Ramaswami, S Minakshisundaram, and so on. Vijayaraghavan pursued his PhD under the famous British mathematician, GH Hardy.

I found Perisastri’s lectures on analysis and algebra amazing and he used to add lots of interesting stories on Indian and western mathematicians in his lectures. Then I spent a couple of years as a PhD scholar at the International Institute for Population Sciences in Mumbai, where I got exposed to real-world population analysis. I then moved to Indian Statistical Institute (ISI), Kolkata, as a Senior Research Fellow and later became Visiting Scientist.

At ISI, I primarily worked with JK Ghosh who was instrumental in my move from Mumbai to Kolkata. I closely interacted with many people at ISI and attended analysis and probability classes by eminent teachers like BV Rao and Somesh Bagchi. But I only started appreciating advanced mathematics due to discussions with my hostel friends, especially P Ramu who was then an MTech student at ISI and was trained from the University of Hyderabad and is now a senior scientist at Defense labs in Pune.

In 2002-2004, I was at IISc as a DST fellow in mathematical sciences, where I received early career world-class exposure in biological and engineering sciences research, shaping my interest in this field.

**Was mathematical modelling of diseases actively pursued when you started out?**

In the early 2000s, mathematical modelling of diseases was not an active research field in India; at least I didn’t come across such things. However, I saw potential in it and tried to understand the techniques myself from a few books available in libraries and using my own intuition. My first success came in 1999 when our paper on HIV modelling was published in the prestigious journal *The Lancet,* jointly with SK Hira, a clinician at JJ Hospital in Mumbai.

In the early 2000s, mathematical modelling of diseases was not an active research field in India; at least I didn’t come across such things

I worked with Masayuki Kakehashi of Hiroshima University, Roy M. Anderson (Imperial College London), Philip K Maini (University of Oxford), interacted with Robert M May (University of Oxford) and held a postdoctoral fellowship with Chris Bauch (University of Guelph).

Anderson and May are eminent researchers in modelling diseases from the 1970s, and they worked as senior advisors for the UK government. My close academic association with them helped me understand how mathematical models are used, beyond academic-quality publications. The exposure I gained with Maini’s group shaped my early career foundations in mathematical modelling. All my early career mentors predominantly used deterministic dynamics models [these models predict based on known relationships between states without considering random variations]. I have, over the years, evolved as a proponent of other types of modelling techniques as well, namely, stochastic, graph theory-based, harmonic analysis, hybrid models, and the like.

**What is mathematical modelling and what are the factors you consider before you start modelling diseases? **

For me, mathematical modelling is like approximately translating scientific phenomena or processes, be it in biology, engineering sciences, finance, medicine or physics, into well-defined, one or more mathematical equations. Often these translations are challenging, but sometimes, it can be very obvious. To understand the research question, modellers have to be very flexible in using the right kind of mathematical approaches. The goal is always to fit the model as closely as possible to the real-world process. Models usually consist of parameters and variables, and ideally, parameters obtained are either from raw data or from published literature.

My philosophy is to first have a deep understanding of the key science questions that I am handling. Then, I look for evidence to support the hypothesis and what is unknown around the question that I am handling: Is the question that we are considering worth attempting through a model or not. Once we are satisfied with the discussions, my collaborators and I work on the actual mathematics and other theoretical developments. Accurate predictions using models is the most challenging aspect.

**You said you were at IISc during 2002-2004. What were you working on here?**

During 2002-2004, I was a DST/SERC [Department of Science and Technology/ Science and Engineering Research Board] Fast Track Young Scientist Fellow in the Mathematical Sciences at IISc. I won this fellowship while I was a Visiting Scientist at the Indian Statistical Institute. I was located at the Centre for Ecological Sciences because Vidyanand Nanjundiah, who was then a Professor at IISc, hosted me in his lab to give me excellent exposure to theoretical biology research that they were conducting. During my days at IISc, public health policymakers in India took notice of my work and contacted me to develop models for framing policy in India. It was their initiation and interest which led me to begin practically useful mathematical work.

Around that time, I got to work for the World Bank for the second time. I had won the London Mathematical Society fellowship to be an academic visitor at the University of Oxford and Imperial College, London. By the end of 2003, I was back at IISc and continued collaborating with national AIDS planners and with higher government officials in developing model-based prevention and treatment strategies. And during 2005-2007, when I was again at Oxford University, the National AIDS Control Policy team asked me to develop models for the third round of policy for the period 2006-2011, which I led from Oxford.

Besides research at IISc, I also taught courses for the Integrated PhD and regular PhD students at IISc, some of it with NV Joshi [Centre for Ecological Sciences]. For me, the good thing about IISc was that it gave me a world-class platform to think originally and to develop scientific professionalism, and of course, it gave me close friends in almost every branch of science and engineering, and in life.

And during 2005-2007, when I was again at Oxford University, the National AIDS Control Policy team asked me to develop models for the third round of policy for the period 2006-2011, which I led from Oxford

**Was the modelling for World Bank similar to AIDS modelling for the Indian government? **

Both projects involved differential equation-type modelling and a bit of statistical setting. In my first assignment as a consultant to the World Bank (while I was a visitor at Imperial College, London before joining IISc), the purpose was to predict the impact of antiretroviral therapies in India for controlling HIV spread. And for my second assignment for them (while I was at IISc), I was asked to develop model-based projections for the district-level spread of HIV in India.

**Could you please explain the model you developed for the Indian government and how it fed into the budget allocation for AIDS control?**

Our aim was to understand the impact of the second and third phase of national AIDS control policies in controlling the spread of HIV in India. The co-authors of these papers were Drs T Kurien, R Bhat, K Sudhakar, and PK Maini. In our first paper that came out in *Mathematical Biosciences and Engineering* (2009), we focused on modelling of HIV transmission dynamics within sub-populations of India (without measuring the role of antiretroviral treatment). In our second paper, published in the *Notices of the American Mathematical Society *(2012), we built, for the first time, models to project the number of HIV individuals in India who require second-line therapy. We had contributed to the fourth round of AIDS policies in India, working as a faculty from ISI.

Once we project the number of individuals who require a certain type of treatment, the government uses these numbers in preparing budgets, based on data for treatment costs per person.

Once we project the number of individuals who require a certain type of treatment, the government uses these numbers in preparing budgets, based on data for treatment costs per person

**Your model for AIDS control was close to the real estimate. Have you had experiences where your model didn’t make the right predictions?**

That’s correct – our projection was close to the real estimate.

When the basic data for a disease is not available, there is not enough data to support accurate transmission dynamics. And when infection causes are unknown, we fail to build accurate and timely models, for example, for the Nipah virus outbreak in 2018 in India.

**Are you still associated with the project on modelling of AIDS and other diseases in India? **

Yes, I am involved in several practically useful and implementable modelling of AIDS and other diseases in India, and also in the USA. Recently when I visited India in the summer of 2018, I had given a talk organised at the National Institution for Transforming India (NITI Aayog, New Delhi) titled “Mathematical Modelling in Government Policy Formations”.

**Are people opening up to the interdisciplinary mode of approach that mathematical modelling of diseases demands?**

I assume so. I would think mathematical modelling is a very important and useful way to handle real-world phenomena because it has the flexibility to blend with computational tools and data science. Pure mathematical modelling without any aim of real-world implementable solutions might be fruitful academically, but for the advancement of science and the well-being of society, an interdisciplinary approach is needed.

I would think mathematical modelling is a very important and useful way to handle real-world phenomena because it has the flexibility to blend with computational tools and data science

Credit for the practical success of our HIV mathematical models must also go to my collaborators, especially non-mathematicians, who put in an enormous amount of effort in back-and-forth discussions.

**What are you currently working on? **

I am heading the Laboratory for Theory and Mathematical Modeling, which I founded, within the Medical College of Georgia at our university, to do practically useful work and also, in the process, set up a math-tech company*. *In 2018, I invented a new technology which developed hybrid models that work with blockchain technology data (with JA Vazquez and L Ostrosky). This technology can save patients’ lives with timely initiation of treatment for certain fungal infections, where the window of opportunity for treatment is shorter. We are working with our university’s office of innovation and commercialisation to file a US Patent for this technology. A new collaborative work on harmonic analysis applications is in progress (with SG Krantz, my hero in mathematics since my postdoc days, whose books are very popular), and we already have our first paper, in 2018.

A few years ago, I proved a theorem, the Carey-Rao Theorem in stationary populations, jointly with biologist JR Carey, and we are working on several theoretical applications of it, and also handling disease modelling projects. Other models for infertility treatment, and graph theory models for bird behaviours and the like, are in progress, with my other collaborators.