The majority of epidemic models are described by non-linear differential equations which do not have a closed-form solution. Due to the absence of a closed-form solution, the understanding of the precise dynamics of a virus is rather limited. We solve the differential equations of the N-intertwined mean-field approximation of the susceptible-infected-susceptible epidemic process with heterogeneous spreading parameters around the epidemic threshold for an arbitrary contact network, provided that the initial viral state vector is small or parallel to the steady-state vector. Numerical simulations demonstrate that the solution around the epidemic threshold is accurate, also above the epidemic threshold and for general initial viral states that are below the steady-state.

多数流行病模型由不具有封闭形式解的非线性微分方程描述。由于不存在封闭形式的解决方案，因此对病毒精确动态的理解相当有限。我们以任意接触网络的流行阈值为中心，以围绕流行阈值的异构扩散参数，对易感性感染易感流行过程的N交织平均场近似的微分方程进行求解，前提是初始病毒状态向量较小或与稳态向量。数值模拟表明，在流行阈值附近的解决方案是准确的，也高于流行阈值，并且对于低于稳态的一般初始病毒状态也是如此。