Epidemic spreading on multilayer homogeneous evolving networks

Markovian Approach for Exploring Competitive Diseases with Heterogeneity-Evidence from COVID-19 and Influenza in China

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

Reactive-diffusion epidemic model on human mobility networks: Analysis and applications to COVID-19 in China

The complex dynamics of human mobility, combined with sporadic cases of local outbreaks, make assessing the impact of large-scale social distancing on COVID-19 propagation in China a challenge. In this paper, with the travel big dataset supported by Baidu migration platform, we develop a reactive-diffusion epidemic model on human mobility networks to characterize the spatio-temporal propagation of COVID-19, and a novel time-dependent function is incorporated into the model to describe the effects of human intervention. By applying the system control theory, we discuss both constant and time-varying threshold behavior of proposed model. In the context of population mobility-mediated epidemics in China, we explore the transmission patterns of COVID-19 in city clusters. The results suggest that human intervention significantly inhibits the high correlation between population mobility and infection cases. Furthermore, by simulating different population flow scenarios, we reveal spatial diffusion phenomenon of cases from cities with high infection density to cities with low infection density. Finally, our model exhibits acceptable prediction performance using actual case data. The localized analytical results verify the ability of the PDE model to correctly describe the epidemic propagation and provide new insights for controlling the spread of COVID-19.

Simplicial epidemic model with birth and death

In this paper, we propose a simplicial susceptible-infected-susceptible (SIS) epidemic model with birth and death to describe epidemic spreading based on group interactions, accompanying with birth and death. The site-based evolutions are formulated by the quenched mean-field probability equations for each site, which is a high-dimensional differential system. To facilitate a theoretical analysis of the influence of system parameters on dynamics, we adopt the mean-field method for our model to reduce the dimension. As a consequence, it suggests that birth and death rates influence the existence and stability of equilibria, as well as the appearance of a bistable state (the coexistence of the stable disease-free and endemic states), which is then confirmed by extensive simulations on empirical and synthetic networks. Furthermore, we find that another type of the bistable state in which a stable periodic outbreak state coexists with a steady disease-free state also emerges when birth and death rates and other parameters satisfy the certain conditions. Finally, we illustrate how the birth and death rates shift the density of infected nodes in the stationary state and the outbreak threshold, which is also verified by sensitivity analysis for the proposed model.