Towards formal probabilistic models for progression of diseases

Diseases such as cancers are among the top killers in many countries, causing tens of thousands of premature deaths worldwide. Unlike many contagious diseases, however, many types of cancers often exhibit clear progression patterns in progression such that early detection can improve the odds of a patientpsilas survival. In fact, even total recovery is possible in some cases. Precise modelling of cancer progression can therefore potentially reduce the number of deaths caused by cancer. In an effort to contribute towards better modelling, this paper presents a two-step formal probabilistic model to describe the progression of cancers. In the first step, we develop a formal functional model using communicating sequential processes (CSP), which is a well-established formal description language for reasoning about concurrency and state machines. In particular, we map various cancer progression stages to states and then we introduce probabilistic behaviors to model state transition in the second step. Where probability distributions are available, the resultant model can then be used to extract quantitative information such as the expected time to terminal stage or death from the time when the cancer is first diagnosed.