diff --git a/docs/epidemic_spreading/markov.rst b/docs/epidemic_spreading/markov.rst index a5c1274..f2eefe8 100644 --- a/docs/epidemic_spreading/markov.rst +++ b/docs/epidemic_spreading/markov.rst @@ -5,7 +5,12 @@ In contrast to Gillespie's simulation one can write down an approximate equation for the temporal evolution of the nodes' probability to be infected, (see Eq. (1) in `Epidemic Threshold in Continuous-Time Evolving Networks`_) which can then be integrated. This is slower than the Gillespie simulation but leads to smaller -fluctuations which makes it easier to obtain the epidemic threshold. +fluctuations which makes it easier to obtain the epidemic threshold. It is based +on the assumption that neighboring infections states are uncorrelated and factorize to +:math:`\left< i_u i_v\right>=\left< i_u \right>\left`. This assumption is +usually justified in non-sparse annealed systems but leads to drastic differences +in other systems. Since temporal contact networks are often neither, use this +model with care. How it works ------------ @@ -18,10 +23,15 @@ governed by .. math:: - p_u(t+\Delta t) = p_u(t) (1-\varrho\Delta t) + (1-p_u(t)) - \left[ - 1-\prod_{v=1}^N(1-\eta\Delta t A_{vu}(t)p_v(t)) - \right] + p_u(t+\Delta t) = 1 - q_u(t,\Delta t)\times\Big[1-p_u(t)\times\left(1-\varrho\Delta t\right)\Big] + +where + +.. math:: + + q_u(t, \Delta t) = \prod_{v=1}^N\Big[1-\eta\Delta t A_{uv}(t)p_v(t)\Big] + +is the probability that none of `u`'s neighbors infects `u` during this time step. Here, :math:`\Delta t=\mathrm{min}\{\Delta t_{\mathrm{network\ change}}, \Delta t_{\mathrm{max}}\}` is either the time until the network changes next, or the maximally allowed diff --git a/docs/reference/_generate/_tacoma.EdgeActivityModel.rst b/docs/reference/_generate/_tacoma.EdgeActivityModel.rst index e1fdb30..62dbb4c 100644 --- a/docs/reference/_generate/_tacoma.EdgeActivityModel.rst +++ b/docs/reference/_generate/_tacoma.EdgeActivityModel.rst @@ -14,7 +14,9 @@ .. autosummary:: ~EdgeActivityModel.__init__ + ~EdgeActivityModel.get_current_edgelist ~EdgeActivityModel.set_initial_configuration + ~EdgeActivityModel.set_initial_edgelist