My research theme focuses on understanding complex systems across various spatio-temporal scales through mathematical modeling. I explore fundamental questions such as:
How a population responds to an epidemic threat?
When is getting vaccinated most cost effective?
Can bacteria provide protection to each other?
What gives rise to re-emergence of diseases?
These questions are pertinent to numerous public health challenges, many of which I have addressed in my previous work.
Can we protect the medicines that protects us? To answer this question, understanding complexities at the population level are not enough, it is important not to overlook the role of pathogen in the spread and evolution of an infectious diseases. For my second postdoctoral research at the University of Michigan, I combined in vitro experiments with mathematical modeling to investigate how the spatiotemporal dynamics of enterococcus faecalis (E. faecalis) communities is affected by exposure to antibiotics.
Using game theoretical formulation of strategic interactions among individuals, I developed an integrated model of an epidemic spreading on a social network, where agents make informed decisions on whether to be vaccinated. I used the Gillespie stochastic evolution algorithm to simulate co-evolution of the epidemic process and vaccine uptake behavior on the social contact network constructed using data collected from 75 villages in India. An important finding from this work is that the prevalence aggregated over the whole population can result in a false perception of low-risk, and therefore can lead to sub-optimal epidemic outcome. Our results underscore the importance of heterogeneity in contact network and the individual-level response in shaping the epidemic at population level.
Epidemic models have become a sophisticated tools for assisting public health decisions and policies in many countries worldwide. Yet fundamental limitations remain in how well these models capture a key social parameter- human behavior. In the last decade, there has been an increase in awareness that in these sophisticated epidemic models there is a neglected dimension of complexity, which is critical to understand the mechanisms underlying infection transmission and control, i.e. how people react to an epidemic threat? In my doctoral work at Banaras Hindu University, I modified classical epidemic models to understand how collective behavioral responses can affect the disease transmission in a population. I teased out the effect of this feedback on the epidemic dynamics in terms of properties of associated systems of differential equations such as, stability and bifurcation. We established that mass-media induced behavioral responses can destabilize the system and push the epidemic trajectory to a limit cycle, i.e., make the epidemic recurrent. Our approach was later adopted by many groups for modeling such systems. We also extended these model to study similar properties of a vector-borne disease and derived the necessary conditions for optimization of behavior-contagion model, using Pontryagin's maximum principle. These dynamical systems are analytically tractable, and hence serves as a wonderful playground for applied mathematicians.