Dynamics analysis of SIR epidemic model with correlation coefficients and clustering coefficient in networks

Pattern mechanism in stochastic SIR networks with ER connectivity

The diffusion of the susceptible and infected is a vital factor in spreading infectious diseases. However, the previous SIR networks cannot explain the dynamical mechanism of periodic behavior and endemic diseases. Here, we incorporate the diffusion and network effect into the SIR model and describes the mechanism of periodic behavior and endemic diseases through wavenumber and saddle-node bifurcation. We also introduce the standard network structured entropy (NSE) and demonstrate diffusion effect could induce the saddle-node bifurcation and Turing instability. Then we reveal the mechanism of the periodic outbreak and endemic diseases by the mean-field method. We provide the Turing instability condition through wavenumber in this network-organized SIR model. In the end, the data from COVID-19 authenticated the theoretical results.

How reported outbreak data can shape individual behavior in a social world

Agencies reporting on disease outbreaks face many choices about what to report and the scale of its dissemination. Reporting impacts an epidemic by influencing individual decisions directly, and the social network in which they are made. We simulated a dynamic multiplex network model—with coupled infection and communication layers—to examine behavioral impacts from the nature and scale of epidemiological information reporting. We explored how adherence to protective behaviors (social distancing) can be facilitated through epidemiological reporting, social construction of perceived risk, and local monitoring of direct connections, but eroded via social reassurance. We varied reported information (total active cases, daily new cases, hospitalizations, hospital capacity exceeded, or deaths) at one of two scales (population level or community level). Total active and new case reporting at the population level were the most effective approaches, relative to the other reporting approaches. Case reporting, which synergizes with test-trace-and-isolate and vaccination policies, should remain a priority throughout an epidemic.

Improving pandemic mitigation policies across communities through coupled dynamics of risk perception and infection

Capturing the coupled dynamics between individual behavioural decisions that affect disease transmission and the epidemiology of outbreaks is critical to pandemic mitigation strategy. We develop a multiplex network approach to model how adherence to health-protective behaviours that impact COVID-19 spread are shaped by perceived risks and resulting community norms. We focus on three synergistic dynamics governing individual behavioural choices: (i) social construction of concern, (ii) awareness of disease incidence, and (iii) reassurance by lack of disease. We show why policies enacted early or broadly can cause communities to become reassured and therefore unwilling to maintain or adopt actions. Public health policies for which success relies on collective action should therefore exploit the behaviourally receptive phase; the period between the generation of sufficient concern to foster adoption of novel actions and the relaxation of adherence driven by reassurance fostered by avoidance of negative outcomes over time.

Disease dynamics and mean field models for clustered networks

Social networks are clustered networks with short mean path length. In this work we analyze the disease dynamics in a class of this type of small-world networks composed of set of households and a set of workplaces. Individuals from each household are randomly assigned to workplaces. In both environments we assumed complete mixing and therefore we obtain highly clustered networks with short mean path lengths. Basic reproduction numbers were computed numerically and we show that at endemic equilibrium the average susceptible proportion <S/N> is different from the inverse of the basic reproduction number (R₀^-1). Therefore exist an exponent p≠1 for which <S/N>^p=R₀^-1. Using this exponent we developed a mean field model which closely capture the disease dynamics in the network. Finally we outline how this model could be use to model vector-borne diseases in social networks.