Mutually cooperative epidemics on power-law networks

Abstract

The spread of an infectious disease can, in some cases, promote the propagation of other pathogens favoring violent outbreaks, which cause a discontinuous transition to an endemic state. The topology of the contact network plays a crucial role in these cooperative dynamics. We consider a susceptible-infected-removed-type model with two mutually cooperative pathogens: An individual already infected with one disease has an increased probability of getting infected by the other. We present a heterogeneous mean-field theoretical approach to the coinfection dynamics on generic uncorrelated power-law degree-distributed networks and validate its results by means of numerical simulations. We show that, when the second moment of the degree distribution is finite, the epidemic transition is continuous for low cooperativity, while it is discontinuous when cooperativity is sufficiently high. For scale-free networks, i.e., topologies with diverging second moment, the transition is instead always continuous. In this way we clarify the effect of heterogeneity and system size on the nature of the transition, and we validate the physical interpretation about the origin of the discontinuity.

Fundamental properties of cooperative contagion processes

“…Only recently, cooperative contagion in which infection with one transmissible agent facilitates infection with another was investigated [36][37][38][39][40][41][42][43][44][45][46][47]. These studies mainly focused on transient dynamics of the generic susceptible-infected-recovery (SIR) model in which individuals acquire immunity after infection.…”

“…This model exhibits avalanche-like outbreak scenarios, depending on the level of cooperation and the structure of the underlying transmission network. Analytical insights [44] have been obtained that explain the role of network topology in cooperative bond percolation systems, in multiplex systems [45], power-law networks [43], as well as sequential coinfection on Poisson networks [37]. Furthermore, it has been found that highly clustered structures in population aid the proliferation of coinfections, contrary to the effect observed in single disease dynamics [41].…”

Risk of Coinfection Outbreaks in Temporal Networks: A Case Study of a Hospital Contact Network

“…This leads to two possible solutions for ρ ab in the region above, but close to the epidemic threshold: if both diseases are not able to meet, ρ ab ≈ 0, while if they meet, ρ ab has a high value. In fact, finite system size effects may hide the broad jumps, appearing even in networks with broad degree distributions [32]. In our case, similar mechanisms, including the influence of the temporal connectivity pattern, explain how the cooperative interaction reinforces the upper endemic branch: infections spread together in the temporal clusters associated with high activity periods, while the night valley of activity and the stochastic recovery allow diseases to separate and spread independently, leading to macroscopic coinfection effects in ρ ab for the cases in which diseases meet again.…”

Persistent spatial patterns of interacting contagions

“…Well-known examples include the case * chenl@snnu.edu.cn of pneumonia bacterium like Streptococcus pneumoniae and viral respiratory illness (e.g., seasonal influenza) where they mutually facilitate each other's propogation [21,22], and the coinfection between human immunodeficiency virus and a host of other infections [23][24][25][26][27]. The interaction among different infections can be either competitive [28][29][30][31][32][33][34] (they suppress each other's circulation) or cooperative [35][36][37][38][39][40][41][42] (they support each other). The mean-field treatment and percolation studies of structured population reveal a rich spectrum of new dynamical features that are unexpected in the classic scenario of single infection.…”