Epidemiology as an empirical science has developed sophisticated methods to measure the causes and patterns of disease in populations. Nevertheless, for many diseases in many countries only partial data are available. When the partial data are insufficient, but data collection is not an option, it is possible to supplement the data by exploiting the causal relations between the various variables that describe a disease process. We present a simple generic disease model with incidence, one prevalent state, and case fatality and remission. We derive a set of equations that describes this disease process and allows calculation of the complete epidemiology of a disease given a minimum of three input variables. We give the example of asthma with age-specific prevalence, remission, and mortality as inputs. Outputs are incidence and case fatality, among others. The set of equations is embedded in a software package called 'DisMod II', which is made available to the public domain by the World Health Organization.