Temperature sensitivity of pest reproductive numbers in age-structured PDE models, with a focus on the invasive spotted lanternfly

TL;DR

This study models the temperature-dependent reproductive dynamics of the invasive spotted lanternfly using a PDE framework, revealing how temperature variations influence pest establishment and control strategies.

Contribution

It introduces a novel PDE model incorporating age structure, diapause, and temperature effects, with a new moving mesh method and a spectral reproductive number analysis.

Findings

Reproductive number $R_0$ is sensitive to temperature variations.

Low-rank structure of the solution operator is identified under certain conditions.

Model calibration aligns with experimental and field data.

Abstract

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.