Modeling transmission of directly transmitted infectious diseases using colored stochastic Petri nets.

In order to improve our understanding of directly transmitted pathogens within host populations, epidemic models should take into account individual heterogeneities as well as stochastic fluctuations in individual parameters. The associated cost results in an increasing level of complexity of the mathematical models which generally lack consistent formalisms. In this paper, we demonstrate that complex epidemic models could be expressed as colored stochastic Petri nets (CSPN). CSPN is a mathematical tool developed in computer science. The concept is based on the Markov Chain theory and on a standard well codified graphical formalism. This approach presents an alternative to other computer simulation methods since it offers both a theoretical formalism and a graphical representation that facilitate the implementation, the understanding and thus the replication or modification of the model. We explain how common concepts of epidemic models--such as the incidence function--can be easily translated into an individual based point of view in the CSPN formalism. We then illustrate this approach by using the well documented susceptible-infected model with recruitment and death.