Comparing the sustainability of different action policy possibilities: Application to the issue of both household survival and forest preservation in the corridor of Fianarantsoa

- Evaluating the sustainability according to different action policy possibilities is crucial.
- Belonging to viability kernel allows distinguishing sustainable situations.
- Minimal admissible control sets that make a given situation sustainable are computed.
- Particular sustainable control functions are exhibited.

A sustainability issue for the rain forest in the corridor of Fianarantsoa (Madagascar) is to preserve the forest while ensuring the development of the local population. The aim of this paper is to determine whether the current situation is sustainable or not according to different action policy possibilities. We propose a general procedure based on viability analysis: Translation of sustainability issues into constraints on the system state; elaboration of a mathematical model of system evolution rules in the form of controlled dynamical system; computations of the viability kernels according to different action policy possibilities. Among control variables, we focus on monetary transfer. Without monetary transfer, we show that the current situation of the rain forest corridor is not sustainable in our mathematical modeling framework. We then estimate the minimal maximal amount per year necessary to make the current situation sustainable.