Modeling and analysis of epidemic processes over large networks from limited data

Abstract

Networks are ubiquitous in today's interlinked world, allowing various types of flow along with their links, for instance, rumor, knowledge, norms (social networks), electricity (power grid), money (financial networks), goods (trade networks), and infectious pathogens (disease networks). In particular, network epidemic models offer analytical and numerical platforms to quantify and forecast the transmission of a pathogen. In this context, a network is a structure of nodes and links, where nodes can represent individuals, locations, or groups, and links can represent physical contacts between individuals, movement flows between locations, or interaction between groups. Studying infectious disease dispersal with network epidemic models is a powerful application of network science. An extremely challenging aspect of studying infectious pathogen dispersal is the insufficient knowledge of the underlying network or unknown epidemic model parameters. Sometimes networks are unattainable because of data privacy, lack of data integrity, missing data, or lack of higher resource requirements. Our research provides a guideline to study epidemic processes on a network from limited available data. In the USA, no mandatory livestock regulatory system exists because of a cultural preference for privacy. We propose a general algorithm to develop a livestock movement network from the limited available data to fill this gap. In this network, nodes represent livestock subpopulations, and links represent livestock directional movements between subpopulations. Network centrality measures are beneficial to understand the contact pattern of a movement network and can assist in detecting the superspreader nodes, which play a critical role in the movement flows and disease transmission. Understanding the role of superspreaders in a movement network is useful for policymakers to control disease outbreaks efficiently. This is possible because the network centrality analysis in the livestock movement network reveals small-world phenomena in the US livestock industry. Individual-based network models are becoming popular due to their capability to integrate heterogeneous social mixing. However, individual contact networks are not available because of privacy concerns. Our research offers an age-specific multilayer individual-based contact network developed from demographic data and Google mobility data. Combining this network with an epidemic model led to costs and benefits of contact tracing being investigated as a key mitigation strategy in the COVID-19 transmission. Then, an approximate Bayesian computation based on a sequential Monte Carlo sampling (ABC-SMC) method allowed network models to estimate the disease propagation rate from the COVID-19 incidence data. The ABC-SMC method is ideal for parameter estimation and model selection of a complex system when the likelihood function is intractable or computationally expensive to evaluate. This work provides a general, flexible, and complete framework to study an epidemic process from data at the individual level. Some individual contact networks have an enormous set of nodes/agents; however, individual-based stochastic epidemic modeling, like the generalized epidemic modeling framework (GEMF), over those vast networks is computationally expensive and time-consuming. We develop a group-based continuous-time Markov epidemic model framework to reduce the computational time of the individual-based framework (GEMF) by reducing the state-space in the Markov chain. The number of states in the individual-based Markov model is M^N (where M is the number of compartments, and N is the number of nodes), and it increases exponentially with the number of nodes N. By partitioning the nodes into C disjointed groups, the group-based approach reduces the state-space to [∏_(i=1)^C((N_i+M-1)/(M-1)) ], which is already polynomial in N for a constant number of groups and quasi-polynomial in N for a logarithmic number of groups; i.e., C=O(log⁡N). Here, N_i represents the number of nodes in a group i and i=1,2,….,C. The simulation results reveal that the accuracy of the group-based approach depends on the network structures and grouping approaches. In summary, our research enhances the current knowledge of network epidemic models both in application and theory; therefore, it can serve as a foundation work of follow-on efforts related to the network epidemic modeling over large networks.