Cooperative contagion processes

based on Li Chen et al., Phase transitions and hysteresis of cooperative contagion processes (http://arxiv.org/abs/1603.09082, 2016)
The majority of epidemic models are designed to capture epidemiological dynamics of single pathogen species in a host population, characterized by epidemiological parameters associated with a single virus or bacterium. However, bacterial and viral pathogens generically interact, either directly or indirectly by means of their effects on the host. Prominent examples are HIV infections that through immune suppression increase the host’s susceptibility towards other infections.

In a simple dynamical system we investigated the effects of cooperation between two pathogens A and B. If a host is infected by one of the diseases, this increases the susceptibility towards the other infection. This is quantified by a cooperativity coefficient C. Both diseases have identical, basic reproduction ratios R0 and recovery rates.

In a stochastic lattice model, each node corresponds to an individual in a population and interacts with it’s neighbors. Nodes can be in 4 different states, S = susceptible, A = infected with A, B = infected with B and AB infected with both. A cooperativity coefficient C = 1 corresponds to a situation in which A and B do not interact, i.e. the infection with one disease is unaltered by an infection with the other. If, however C > 1, infection with one disease facilitates infection with the other.

Many effects emerge when C > 1, that are absent in single or independent contagion processes. First, when C > 1, a region for R0 exists, in which the system exhibits two stable states, one in which both diseases prevail and one disease-free state. This state is observed for R0 < 1 even. When R0 > 0, any initial condition explodes into a state that is dominated by coinfections. This transition is of first order.

The tool below illustrates these effects in an interactive framework.
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