THE CONTINUOUS AND IMPULSIVE GRAZING MODEL IN A SAHELIAN REGION

Pastoralism in the Sahel plays a major role in the economy of West African countries. With a wide diversity of livestock species, it contributes to the food and nutritional security of rural and urban households. So, for reasons of survival, the shepherd can harvest from the herd population. Thus, in this paper, we build and analyze a hybrid mathematical model of resource-herd interactions in a Sahelian region by first taking into account a continuous harvest for various needs. As several months, or even years, can elapse between two harvests, it is more realistic to consider that this harvesting takes place impulsively, as it very often occurs at specific times for known reasons (sale, bequest, slaughter, etc.). We have carried out a qualitative analysis of our model, and numerical simulations are provided to illustrate our theoretical results and support the discussion. theoretical results and support the discussion.