  Production-destruction systems (PDS) of ordinary differential equations
(ODEs) are used to describe physical and biological reactions in nature. The
considered quantities are subject to natural laws. Therefore, they preserve
positivity and conservation of mass at the analytical level. In order to
maintain these properties at the discrete level, the so-called modified
Patankar-Runge-Kutta (MPRK) schemes are often used in this context. However, up
to our knowledge, the family of MPRK has been only developed up to third order
of accuracy. In this work, we propose a method to solve PDS problems, but using
the Deferred Correction (DeC) process as a time integration method. Applying
the modified Patankar approach to the DeC scheme results in provable
conservative and positivity preserving methods. Furthermore, we demonstrate
that these modified Patankar DeC schemes can be constructed up to arbitrarily
high order. Finally, we validate our theoretical analysis through numerical
simulations.
