  We present a Virtual Element Method (VEM) for a nonlocal reaction-diffusion
system of the cardiac electric field. To this system, we analyze an
$H^1(\Omega)$-conforming discretization by means of VEM which can make use of
general polygonal meshes. Under standard assumptions on the computational
domain, we establish the convergence of the discrete solution by considering a
series of a priori estimates and by using a general $L^p$ compactness
criterion. Moreover, we obtain optimal order space-time error estimates in the
$L^2$ norm. Finally, we report some numerical tests supporting the theoretical
results.
