Infectious Disease Spread through Indian Transportation Network

Abstract

We study infectious disease spread through the Indian transportation network in this thesis. We use a hazard index to quantify the risk faced by 446 Indian cities for an epidemic starting from any city. This hazard index, also called as effective distance was first introduced by Helbing and Brockmann to explain the global spread of infectious diseases. Even though there have been a lot of India-specific studies to examine and predict the spread of infection, to our knowledge, none of them consider long-distance travel through multiple modes of transportation as the primary source of infection. We estimate the traffic for three modes of transport – air, rail, and road to construct the transportation network for India. We use the Susceptible-Infected-Recovered (SIR) metapopulation model to simulate the dynamical system and quantify the associated risk by the arrival time of the infection to the city. We show that the effective distance is an objectively better hazard index than geographical distance and that it works the best for higher values of SIR infection rate parameters and lower threshold of infected cases to define arrival time. We also illustrate that effective distance can be modified to cover the case of multiple outbreak locations. Before comparing with the real-life data of Covid-19 cases, we give evidence for removing critical links using the link salience treatment to curb the spread of the disease. Finally, we show that the SIR metapopulation model has some static and dynamical properties similar to the Fisher-KPP class of equations through numerical simulations. Our study opens up multiple new avenues to build a full-scale working model for India with better mobility and traffic data and study diffusion-like processes on heterogeneous networks.