Mathematical Model of Basal Sprout Production in Vector-Borne Tree Disease

Abstract

Some tree species respond to disease by producing basal sprouts from the base and root system of a dying tree, which can alter disease dynamics by altering demography. In the case of many lethal, airborne tree diseases, the production of basal sprouts can be a key contributor to population resurgence post-epidemic, but the effect in lethal, vector-borne tree diseases has not yet been studied. To determine the role of basal sprout production and secondary infection via the root system of infected parent trees in lethal, vector-borne tree diseases, we develop a stage-structured SI-X mathematical model and use laurel wilt, a vector-borne tree disease in which infected trees provide suitable material for vector reproduction, as our model system. The mathematical model shows that the production and secondary infection of basal sprouts do not affect the short-term dynamics of laurel wilt but profoundly alter the long-term dynamics of the laurel wilt epidemic. In particular, in the absence of basal sprout infection, basal sprout production yields a larger host population after disease establishment, but as secondary infection increases, the utility of basal sprouts to maintain the host population decreases. Results suggest management strategies for lethal, vector-borne diseases should depend on the ratio of the basal sprout production rate to the secondary infection rate.

Dynamic Analysis of a Delayed Differential Equation for Ips subelongatus Motschulsky-Larix spp.

“…To address the issue of forest pests and diseases, an important approach in the field of mathematics is to establish mathematical models for simulating these problems. Various models of forest diseases and pests have been studied [11][12][13]. Many scholars provided a theoretical analysis of the models from an equation analysis perspective [14][15][16][17][18].…”