Local and global epidemic outbreaks in populations moving in inhomogeneous environments

Feedback Loops in Opinion Dynamics of Agent-Based Models with Multiplicative Noise

We introduce an agent-based model for co-evolving opinions and social dynamics, under the influence of multiplicative noise. In this model, every agent is characterized by a position in a social space and a continuous opinion state variable. Agents' movements are governed by the positions and opinions of other agents and similarly, the opinion dynamics are influenced by agents' spatial proximity and their opinion similarity. Using numerical simulations and formal analyses, we study this feedback loop between opinion dynamics and the mobility of agents in a social space. We investigate the behaviour of this ABM in different regimes and explore the influence of various factors on the appearance of emerging phenomena such as group formation and opinion consensus. We study the empirical distribution, and, in the limit of infinite number of agents, we derive a corresponding reduced model given by a partial differential equation (PDE). Finally, using numerical examples, we show that a resulting PDE model is a good approximation of the original ABM.

A multi-agent model to study epidemic spreading and vaccination strategies in an urban-like environment

Worldwide urbanization calls for a deeper understanding of epidemic spreading within urban environments. Here, we tackle this problem through an agent-based model, in which agents move in a two-dimensional physical space and interact according to proximity criteria. The planar space comprises several locations, which represent bounded regions of the urban space. Based on empirical evidence, we consider locations of different density and place them in a core-periphery structure, with higher density in the central areas and lower density in the peripheral ones. Each agent is assigned to a base location, which represents where their home is. Through analytical tools and numerical techniques, we study the formation mechanism of the network of contacts, which is characterized by the emergence of heterogeneous interaction patterns. We put forward an extensive simulation campaign to analyze the onset and evolution of contagious diseases spreading in the urban environment. Interestingly, we find that, in the presence of a core-periphery structure, the diffusion of the disease is not affected by the time agents spend inside their base location before leaving it, but it is influenced by their motion outside their base location: a strong tendency to return to the base location favors the spreading of the disease. A simplified one-dimensional version of the model is examined to gain analytical insight into the spreading process and support our numerical findings. Finally, we investigate the effectiveness of vaccination campaigns, supporting the intuition that vaccination in central and dense areas should be prioritized.

Epidemic spreading in modular time-varying networks

We investigate the effects of modular and temporal connectivity patterns on epidemic spreading. To this end, we introduce and analytically characterise a model of time-varying networks with tunable modularity. Within this framework, we study the epidemic size of Susceptible-Infected-Recovered, SIR, models and the epidemic threshold of Susceptible-Infected-Susceptible, SIS, models. Interestingly, we find that while the presence of tightly connected clusters inhibits SIR processes, it speeds up SIS phenomena. In this case, we observe that modular structures induce a reduction of the threshold with respect to time-varying networks without communities. We confirm the theoretical results by means of extensive numerical simulations both on synthetic graphs as well as on a real modular and temporal network.

Human mobility networks and persistence of rapidly mutating pathogens

Rapidly mutating pathogens may be able to persist in the population and reach an endemic equilibrium by escaping hosts' acquired immunity. For such diseases, multiple biological, environmental and population-level mechanisms determine the dynamics of the outbreak, including pathogen's epidemiological traits (e.g. transmissibility, infectious period and duration of immunity), seasonality, interaction with other circulating strains and hosts' mixing and spatial fragmentation. Here, we study a susceptible-infected-recovered-susceptible model on a metapopulation where individuals are distributed in sub-populations connected via a network of mobility flows. Through extensive numerical simulations, we explore the phase space of pathogen's persistence and map the dynamical regimes of the pathogen following emergence. Our results show that spatial fragmentation and mobility play a key role in the persistence of the disease whose maximum is reached at intermediate mobility values. We describe the occurrence of different phenomena including local extinction and emergence of epidemic waves, and assess the conditions for large-scale spreading. Findings are highlighted in reference to previous studies and to real scenarios. Our work uncovers the crucial role of hosts' mobility on the ecological dynamics of rapidly mutating pathogens, opening the path for further studies on disease ecology in the presence of a complex and heterogeneous environment.

Emergence of metapopulations and echo chambers in mobile agents

Multi-agent models often describe populations segregated either in the physical space, i.e. subdivided in metapopulations, or in the ecology of opinions, i.e. partitioned in echo chambers. Here we show how both kinds of segregation can emerge from the interplay between homophily and social influence in a simple model of mobile agents endowed with a continuous opinion variable. In the model, physical proximity determines a progressive convergence of opinions but differing opinions result in agents moving away from each others. This feedback between mobility and social dynamics determines the onset of a stable dynamical metapopulation scenario where physically separated groups of like-minded individuals interact with each other through the exchange of agents. The further introduction of confirmation bias in social interactions, defined as the tendency of an individual to favor opinions that match his own, leads to the emergence of echo chambers where different opinions coexist also within the same group. We believe that the model may be of interest to researchers investigating the origin of segregation in the offline and online world.

Discrete-time moment closure models for epidemic spreading in populations of interacting individuals

Understanding the dynamics of spread of infectious diseases between individuals is essential for forecasting the evolution of an epidemic outbreak or for defining intervention policies. The problem is addressed by many approaches including stochastic and deterministic models formulated at diverse scales (individuals, populations) and different levels of detail. Here we consider discrete-time SIR (susceptible-infectious-removed) dynamics propagated on contact networks. We derive a novel set of 'discrete-time moment equations' for the probability of the system states at the level of individual nodes and pairs of nodes. These equations form a set which we close by introducing appropriate approximations of the joint probabilities appearing in them. For the example case of SIR processes, we formulate two types of model, one assuming statistical independence at the level of individuals and one at the level of pairs. From the pair-based model we then derive a model at the level of the population which captures the behavior of epidemics on homogeneous random networks. With respect to their continuous-time counterparts, the models include a larger number of possible transitions from one state to another and joint probabilities with a larger number of individuals. The approach is validated through numerical simulation over different network topologies.