Microsimulation of infectious diseases requires simulation of many life histories of interacting individuals. In particular, relatively rare infections such as leprosy need to be studied in very large populations. Computation time increases disproportionally with the size of the simulated population. We present a novel method, MUSIDH, an acronym for multiple use of simulated demographic histories, to reduce computation time. Demographic history refers to the processes of birth, death and all other demographic events that should be unrelated to the natural course of an infection, thus non-fatal infections. MUSIDH attaches a fixed number of infection histories to each demographic history, and these infection histories interact as if being the infection history of separate individuals. With two examples, mumps and leprosy, we show that the method can give a factor 50 reduction in computation time at the cost of a small loss in precision. The largest reductions are obtained for rare infections with complex demographic histories.