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In this paper, we analyse the structure of the set of positive solutions ofan heterogeneous nonlocal equation of the form: $$ \int_{\Omega} K(x,y)u(y)\,dy -\int_ {\Omega}K(y, x)u(x)\, dy + a_0u+\lambda a_1(x)u-\beta(x)u^p=0 \quad \text{in}\quad \times \O$$ where $\Omega\subset \R^n$ is abounded open set, $K\in C(\R^n\times \R^n) $ is nonnegative, $a_i,\beta \inC(\Omega)$ and $\lambda\in\R$. Such type of equation appears in some studies ofpopulation dynamics where the above solutions are the stationary states of thedynamic of a spatially structured population evolving in a heterogeneouspartially controlled landscape and submitted to a long range dispersal. Undersome fairly general assumptions on $K,a_i$ and $\beta$ we first establish anecessary and sufficient criterium for the existence of a unique positivesolution. Then we analyse the structure of the set of positive solution$(\lambda,u_\lambda)$ with respect to the presence or absence of a refuge zone(i.e $\omega$ so that $\beta_{|\omega}\equiv 0$).

Nonlocal refuge model with a partial control