The impact of spatial and social structure on an SIR epidemic on a weighted multilayer network.

A key factor in the transmission of infectious diseases is the structure of disease transmitting contacts. In the context of the current COVID-19 pandemic and with some data based on the Hungarian population we develop a theoretical epidemic model (susceptible-infected-removed, SIR) on a multilayer network. The layers include the Hungarian household structure, with population divided into children, adults and elderly, as well as schools and workplaces, some spatial embedding and community transmission due to sharing communal spaces, service and public spaces. We investigate the sensitivity of the model (via the time evolution and final size of the epidemic) to the different contact layers and we map out the relation between peak prevalence and final epidemic size. When compared to the classic compartmental model and for the same final epidemic size, we find that epidemics on multilayer network lead to higher peak prevalence meaning that the risk of overwhelming the health care system is higher. Based on our model we found that keeping cliques/bubbles in school as isolated as possible has a major effect while closing workplaces had a mild effect as long as workplaces are of relatively small size.

Epidemic Spreading and Equilibrium Social Distancing in Heterogeneous Networks.

We study a multi-type SIR epidemic process within a heterogeneous population that interacts through a network. We base social contact on a random graph with given vertex degrees, and we give limit theorems on the fraction of infected individuals. For given social distancing individual strategies, we establish the epidemic reproduction number R 0 , which can be used to identify network vulnerability and inform vaccination policies. In the second part of the paper, we study the equilibrium of the social distancing game. Individuals choose their social distancing level according to an anticipated global infection rate, which must equal the actual infection rate following their choices. We give conditions for the existence and uniqueness of an equilibrium. In the case of random regular graphs, we show that voluntary social distancing will always be socially sub-optimal.

Vaccination with partial transmission and social distancing on contact networks

We study the impact of vaccination on the risk of epidemics spreading through structured networks using the cavity method of statistical physics. We relax the assumption that vaccination prevents all transmission of a disease used in previous studies, such that vaccinated nodes have a small probability of transmission. To do so, we extend the cavity method to study networks where nodes have heterogeneous transmissibility. We find that vaccination with partial transmission still provides herd immunity and show how the herd immunity threshold depends upon the assortativity between nodes of different transmissibility. In addition, we study the impact of social distancing via bond percolation and show that percolation targeting links between nodes of high transmissibility can reduce the risk of an epidemic greater than targeting links between nodes of high degree. Finally, we extend recent methods to compute the distributional equations of risk in populations with heterogeneous transmissibility and show how targeted social distancing measures may reduce overall risk greater than untargeted vaccination campaigns, by comparing the effect of random and targeted strategies of node and link deletion on the risk distribution.

Optimal COVID-19 Vaccination Strategies with Limited Vaccine and Delivery Capabilities

We develop a model of infection spread that takes into account the existence of a vulnerable group as well as the variability of the social relations of individuals. We develop a compartmentalized power-law model, with power-law connections between the vulnerable and the general population, considering these connections as well as the connections among the vulnerable as parameters that we vary in our tests. We use the model to study a number of vaccination strategies under two hypotheses: first, we assume a limited availability of vaccine but an infinite vaccination capacity, so all the available doses can be administered in a short time (negligible with respect to the evolution of the epidemic). Then, we assume a limited vaccination capacity, so the doses are administered in a time non-negligible with respect to the evolution of the epidemic. We develop optimal strategies for the various social parameters, where a strategy consists of (1) the fraction of vaccine that is administered to the vulnerable population and (2) the criterion that is used to administer it to the general population. In the case of a limited vaccination capacity, the fraction (1) is a function of time, and we study how to optimize it to obtain a maximal reduction in the number of fatalities. © 2021 ACM.

Switchover phenomenon induced by epidemic seeding on geometric networks.

It is a fundamental question in disease modeling how the initial seeding of an epidemic, spreading over a network, determines its final outcome. One important goal has been to find the seed configuration, which infects the most individuals. Although the identified optimal configurations give insight into how the initial state affects the outcome of an epidemic, they are unlikely to occur in real life. In this paper we identify two important seeding scenarios, both motivated by historical data, that reveal a complex phenomenon. In one scenario, the seeds are concentrated on the central nodes of a network, while in the second one, they are spread uniformly in the population. Comparing the final size of the epidemic started from these two initial conditions through data-driven and synthetic simulations on real and modeled geometric metapopulation networks, we find evidence for a switchover phenomenon: When the basic reproduction number [Formula: see text] is close to its critical value, more individuals become infected in the first seeding scenario, but for larger values of [Formula: see text], the second scenario is more dangerous. We find that the switchover phenomenon is amplified by the geometric nature of the underlying network and confirm our results via mathematically rigorous proofs, by mapping the network epidemic processes to bond percolation. Our results expand on the previous finding that, in the case of a single seed, the first scenario is always more dangerous and further our understanding of why the sizes of consecutive waves of a pandemic can differ even if their epidemic characters are similar.

COVID-19: Analytics of contagion on inhomogeneous random social networks.

Motivated by the need for robust models of the Covid-19 epidemic that adequately reflect the extreme heterogeneity of humans and society, this paper presents a novel framework that treats a population of N individuals as an inhomogeneous random social network (IRSN). The nodes of the network represent individuals of different types and the edges represent significant social relationships. An epidemic is pictured as a contagion process that develops day by day, triggered by a seed infection introduced into the population on day 0. Individuals' social behaviour and health status are assumed to vary randomly within each type, with probability distributions that vary with their type. A formulation and analysis is given for a SEIR (susceptible-exposed-infective-removed) network contagion model, considered as an agent based model, which focusses on the number of people of each type in each compartment each day. The main result is an analytical formula valid in the large N limit for the stochastic state of the system on day t in terms of the initial conditions. The formula involves only one-dimensional integration. The model can be implemented numerically for any number of types by a deterministic algorithm that efficiently incorporates the discrete Fourier transform. While the paper focusses on fundamental properties rather than far ranging applications, a concluding discussion addresses a number of domains, notably public awareness, infectious disease research and public health policy, where the IRSN framework may provide unique insights.

Spreading of infections on random graphs: A percolation-type model for COVID-19.

We introduce an epidemic spreading model on a network using concepts from percolation theory. The model is motivated by discussing the standard SIR model, with extensions to describe effects of lockdowns within a population. The underlying ideas and behaviour of the lattice model, implemented using the same lockdown scheme as for the SIR scheme, are discussed in detail and illustrated with extensive simulations. A comparison between both models is presented for the case of COVID-19 data from the USA. Both fits to the empirical data are very good, but some differences emerge between the two approaches which indicate the usefulness of having an alternative approach to the widespread SIR model.