  Invasive pest establishment is a pervasive threat to global ecosystems,
agriculture, and public health. The recent establishment of the invasive
spotted lanternfly in the northeastern United States has proven devastating to
farms and vineyards, necessitating urgent development of population dynamical
models and effective control practices. In this paper, we propose a stage- and
age-structured system of PDEs to model insect pest populations, in which
underlying dynamics are dictated by ambient temperature through rates of
development, fecundity, and mortality. The model incorporates diapause and
non-diapause pathways, and is calibrated to experimental and field data on the
spotted lanternfly. We develop a novel moving mesh method for capturing
age-advection accurately, even for coarse discretization parameters. We define
a one-year reproductive number ($R_0$) from the spectrum of a one-year solution
operator, and study its sensitivity to variations in the mean and amplitude of
the annual temperature profile. We quantify assumptions sufficient to give rise
to the low-rank structure of the solution operator characteristic of part of
the parameter domain. We discuss establishment potential as it results from the
pairing of a favorable $R_0$ value and transient population survival, and
address implications for pest control strategies.
