Figure 1: SIS Markov chain dynamics. | Scientific Reports

Figure 1: SIS Markov chain dynamics.

From: Disease dynamics in a stochastic network game: a little empathy goes a long way in averting outbreaks

Figure 1

We show one step of the Markov chain dynamics in (a) where circles denote individuals who are healthy (open) or sick (shaded). The edges denote contacts, where the actions are indicated by the edge-end types, social distancing | and interaction . Given the state of the disease and contact network at time t, individuals decide to take preemptive measures or not at time t+ which determines the state of each individual at time t + 1 according to the Markov chain dynamics in (7). If ai = 1, individual i does not take any preemptive measures. If ai = 0, i self-isolates reducing any risk of disease contraction or spread to zero. A healthy individual can only contract the disease from an interaction with a neighbor if and only if the individual’s neighbor is infected and neither of the two self-isolates. These interactions are marked by a red dot in the middle figure. We enumerate each pair of state and action in (b).

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