This explorable illustrates and compares three vaccination strategies in complex networks. In this type of model nodes are people and network links potential transmission paths. “Vaccination” then means that nodes are disconnected from the network because they can no longer acquire or transmit a disease. Vaccination thus effectively dilutes the network. Two strategies, A and B, are straightforward to understand. A third one, C, is a bit odd and counterintuitive at first glance:

This explorable illustrates the mechanism of herd immunity. When an infectious disease spreads in a population, an individual can be protected by a vaccine that delivers immunity. But there’s a greater good. Immunization not only projects the individual directly. The immunized person will also never transmit the disease to others, effectively reducing the likelihood that the disease can proliferate in the population. Because of this, a disease can be eradicated even if not the entire population is immunized. This population wide effect is known as herd immunity.

This explorable illustrates a process known as percolation. Percolation is a topic very important for understanding processes in physics, biology, geology, hydrology, horstology, epidemiology, and other fields. Percolation theory is the mathematical tool designed for understanding these processes.

This explorable illustrates the behavior of a contagion process near its critical point. Contagion processes, for example transmissible infectious diseases, typically exhibit a critical point, a threshold below which the disease will die out, and above which the disease is sustained in a population. Interesting dynamical things happen when the system is near its critical point.

This explorable illustrates the dynamics of the SIRS epidemic model, a generic model that captures disease dynamics in a populations or related contagion phenomena.