SIS Mobility Lab · interactive model
Simulate epidemic dynamics in two connected communities, then connect the trajectories to the threshold and endemic-equilibrium structure.
Active experiment
State view
Patch 1→Patch 2
Patch 1←Patch 2
Simulation output
Endemic-equilibrium (EE) explorer
Drag the gold dS line while the active roots update. Solid branches are stable, dashed branches unstable, and neutral dotted branches numerically indeterminate.
Each node is a community. Its area represents total population, the warm arc represents infection prevalence, and the paired lanes show susceptible and infected movement computed from the active state. The time cursor drives both the network and plot.
dSᵢ/dt = dS Σⱼ LᵢⱼSⱼ − βᵢSᵢIᵢ + γᵢIᵢ
dIᵢ/dt = dI Σⱼ LᵢⱼIⱼ + βᵢSᵢIᵢ − γᵢIᵢ
Mass action: the infection term is βᵢSᵢIᵢ, without division by patch population.R₀ characterizes invasion near the disease-free equilibrium, but it does not by itself describe every endemic equilibrium. In this model dS can alter endemic structure even though it does not enter the next-generation expression for R₀.
At time 0, total infected is 0.3 and total prevalence is 7.5 percent. R zero is 1.2756.