We consider a one-dimensional lattice model with the nearest-neighbour interaction and the next-nearest-neighbour interaction with filling factor 1/2 at zero temperature. The particles are assumed to be spinless fermions or hard-core bosons. Using very simple assumptions we are able to predict the basic structure of the insulator - metal phase diagram for this model. Computations of the flux sensitivity support the main features of the proposed diagram and show that the system maintains metallic properties at arbitrarily large values of and along the line , where J is the hopping amplitude, and . We think that close to this line the system is a `weak' metal in the sense that the flux sensitivity decreases with the size of the system not exponentially but as with .