Munik Shrestha (University of New Mexico; SFI Graduate Fellow)
Abstract. Epidemics is a common out-of-equilibrium phenomena of important interdisciplinary interest. However, compared to dynamics close to equilibrium, development of tools for systems that are far away from equilibrium have been relatively limited. Recently, Dynamic Message-Passing (DMP) has been applied for high accuracy implementation of epidemics dynamics in disordered medium like networks. But, to date, DMP has been restricted to models with only one-way state changes, as opposed to models where nodes can return to previously occupied states. Here, I will present our recent development of DMP for recurrent models such as SIS and SIRS, where multiple waves of infection can pass through the population. We have developed a new class of differential equations for these models. Our methods are much faster than direct simulation, and they are also more simple and efficient than the so-called pair approximations currently used in epidemiology. If time permits, I will also give a brief mention of DMP’s relation with non-backtracking matrix.