Petri nets in epidemiology

Abstract

In this work we study Petri nets associated to ordinary differential equations coming from epidemiological models. We propose a geometric procedure to obtain the basic reproduction number. This number is defined as the average number of secondary individuals during their entire infectious lifetime.

Algorithmic Approach for a Unique Definition of the Next-Generation Matrix

“…Section 4 is dedicated to a host-only model, with a single susceptible class and an F matrix of rank one, where the formula of R 0 may be "guessed by inspection" of the flow chart. These kinds of examples have kept alive the hope of "interpretable R 0 formulas", as illustrated in other recent papers-see for example [18,19]. But in fact, as far as we know, no interpretable R 0 formula has emerged outside the rank one case, which is already fully studied in [20].…”

“…But in fact, as far as we know, no interpretable R 0 formula has emerged outside the rank one case, which is already fully studied in [20]. The papers [18,19] start by presenting simple rank one cases, then proposing algorithms for more complex cases based on the graph structure of the flow chart, which, in our opinion, are not sufficiently detailed or documented. While it may well be that tools like Petri nets, as proposed in the second paper, will one day succeed for resolving flow charts with certain structures, this does not seem to have happened yet.…”