Fundamental properties of cooperative contagion processes

Abstract

We investigate the effects of cooperativity between contagion processes that spread and persist in a host population. We propose and analyze a dynamical model in which individuals that are affected by one transmissible agent A exhibit a higher than baseline propensity of being affected by a second agent B and vice versa. The model is a natural extension of the traditional susceptible-infected-susceptible model used for modeling single contagion processes. We show that cooperativity changes the dynamics of the system considerably when cooperativity is strong. The system exhibits discontinuous phase transitions not observed in single agent contagion, multi-stability, a separation of the traditional epidemic threshold into different thresholds for inception and extinction as well as hysteresis. These properties are robust and are corroborated by stochastic simulations on lattices and generic network topologies. Finally, we investigate wave propagation and transients in a spatially extended version of the model and show that especially for intermediate values of baseline reproduction ratios the system is characterized by various types of wave-front speeds. The system can exhibit spatially heterogeneous stationary states for some parameters and negative front speeds (receding wave fronts). The two agent model can be employed as a starting point for more complex contagion processes, involving several interacting agents, a model framework particularly suitable for modeling the spread and dynamics of microbiological ecosystems in host populations.

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

“…The authors have argued that their model can fall into one of three universal classes, due to the behavior of fixed point curves. Also, in [38][39][40], the authors consider "implicit memory" by applying asynchronous adapting in disease propagation. They show that this type of memory can lead to a first-order phase transition in outbreaks, thus hysteresis can arise in such models [40].…”

Systemic Risks: Theory and Mathematical Modeling

“…[12] Further examples are failures of infrastructure, such as the electrical grid, [13] the break-down of a financial system, [14] or such phenomena as public opinion formation or economic innovations. In the model systems, it has been established that boundary conditions keeping the system away from the dead state of static equilibrium and exceeding threshold values may drive a system into a regime of instability out of which new dynamic structures may suddenly emerge, such as a laser light wave or a chemical structure.…”

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.…”

“…For example, when different infections are competing, both one-infection-dominance and coexistence are possible, depending on the properties of involved infections and the underlining networks [28]. By contrast, in cooperative contagions discontinuous outbreak transition appears [35,36], along with many interesting spreading features such as the higher chance of outbreak in clustered networks [37], firstorder phase transitions in the contagion prevalence [40], etc.…”

“…To our knowledge, there is rare work discussing the spatial dynamics of interacting contagions, especially the possibility of pattern emergence. A preliminary effort studies the spatial dynamics of two interacting contagions, assuming all individuals are of identical mobilities; novel propagation modes are revealed, like receding fronts and standing waves [40]. However, in realistic cases, individuals in different states are generally of different mobilities, depending on the individual's state.…”