Modelling the first wave of COVID-19 in India.

Estimating the burden of COVID-19 in India is difficult because the extent to which cases and deaths have been undercounted is hard to assess. Here, we use a 9-component, age-stratified, contact-structured epidemiological compartmental model, which we call the INDSCI-SIM model, to analyse the first wave of COVID-19 spread in India. We use INDSCI-SIM, together with Bayesian methods, to obtain optimal fits to daily reported cases and deaths across the span of the first wave of the Indian pandemic, over the period Jan 30, 2020 to Feb 15, 2021. We account for lock-downs and other non-pharmaceutical interventions (NPIs), an overall increase in testing as a function of time, the under-counting of cases and deaths, and a range of age-specific infection-fatality ratios. We first use our model to describe data from all individual districts of the state of Karnataka, benchmarking our calculations using data from serological surveys. We then extend this approach to aggregated data for Karnataka state. We model the progress of the pandemic across the cities of Delhi, Mumbai, Pune, Bengaluru and Chennai, and then for India as a whole. We estimate that deaths were undercounted by a factor between 2 and 5 across the span of the first wave, converging on 2.2 as a representative multiplier that accounts for the urban-rural gradient. We also estimate an overall under-counting of cases by a factor of between 20 and 25 towards the end of the first wave. Our estimates of the infection fatality ratio (IFR) are in the range 0.05-0.15, broadly consistent with previous estimates but substantially lower than values that have been estimated for other LMIC countries. We find that approximately 35% of India had been infected overall by the end of the first wave, results broadly consistent with those from serosurveys. These results contribute to the understanding of the long-term trajectory of COVID-19 in India.

Resource dependency and survivability in complex networks.

Components in many real-world complex systems depend on each other for the resources required for survival and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially affects how the resources produced in the system are efficiently shared among its components, which in turn decides a network's survivability. Here we present a simple threshold model that provides insight into this relationship between the network structure and survivability. We show that, as a combined effect of local sharing and finite lifetime of resources, many components in a complex system may die of lack of resources even when a sufficient amount is available in the system. We also obtain a surprising result that although the scale-free networks exhibit a significantly higher survivability compared to their homogeneous counterparts, a vertex in the latter survives longer on average. Finally, we demonstrate that the system's survivability can be substantially improved by changing the way vertices distribute resources among the neighbors. Our work is a step towards understanding the relationship between intricate resource dependencies present in many real-world complex systems and their survivability.

Detecting abnormality in heart dynamics from multifractal analysis of ECG signals.

The characterization of heart dynamics with a view to distinguish abnormal from normal behavior is an interesting topic in clinical sciences. Here we present an analysis of the Electro-cardiogram (ECG) signals from several healthy and unhealthy subjects using the framework of dynamical systems approach to multifractal analysis. Our analysis differs from the conventional nonlinear analysis in that the information contained in the amplitude variations of the signal is being extracted and quantified. The results thus obtained reveal that the attractor underlying the dynamics of the heart has multifractal structure and the variations in the resultant multifractal spectra can clearly separate healthy subjects from unhealthy ones. We use supervised machine learning approach to build a model that predicts the group label of a new subject with very high accuracy on the basis of the multifractal parameters. By comparing the computed indices in the multifractal spectra with that of beat replicated data from the same ECG, we show how each ECG can be checked for variations within itself. The increased variability observed in the measures for the unhealthy cases can be a clinically meaningful index for detecting the abnormal dynamics of the heart.

A random interacting network model for complex networks.

We propose a RAndom Interacting Network (RAIN) model to study the interactions between a pair of complex networks. The model involves two major steps: (i) the selection of a pair of nodes, one from each network, based on intra-network node-based characteristics, and (ii) the placement of a link between selected nodes based on the similarity of their relative importance in their respective networks. Node selection is based on a selection fitness function and node linkage is based on a linkage probability defined on the linkage scores of nodes. The model allows us to relate within-network characteristics to between-network structure. We apply the model to the interaction between the USA and Schengen airline transportation networks (ATNs). Our results indicate that two mechanisms: degree-based preferential node selection and degree-assortative link placement are necessary to replicate the observed inter-network degree distributions as well as the observed inter-network assortativity. The RAIN model offers the possibility to test multiple hypotheses regarding the mechanisms underlying network interactions. It can also incorporate complex interaction topologies. Furthermore, the framework of the RAIN model is general and can be potentially adapted to various real-world complex systems.

Divisibility patterns of natural numbers on a complex network.

Investigation of divisibility properties of natural numbers is one of the most important themes in the theory of numbers. Various tools have been developed over the centuries to discover and study the various patterns in the sequence of natural numbers in the context of divisibility. In the present paper, we study the divisibility of natural numbers using the framework of a growing complex network. In particular, using tools from the field of statistical inference, we show that the network is scale-free but has a non-stationary degree distribution. Along with this, we report a new kind of similarity pattern for the local clustering, which we call "stretching similarity", in this network. We also show that the various characteristics like average degree, global clustering coefficient and assortativity coefficient of the network vary smoothly with the size of the network. Using analytical arguments we estimate the asymptotic behavior of global clustering and average degree which is validated using numerical analysis.