Invasive Stink Bugs and Related Species (Pentatomoidea)

630 Invasive Stink Bugs and Related Species (Pentatomoidea)

rates, which relates to semi-persistently transmitted pathogens. Not surprisingly, infectious vector birth
rates show the opposite effects from vector recovery; as bv increases, the percent of both infected hosts
and vectors increases in a sigmoidal manner (Figure 13.2). Although this model makes many simplify-
ing assumptions of pentatomid ecology, these results may help explain why non-persistently transmitted
pathogens are relatively rare among the Pentatomidae (Mitchell 2004).

13.7.2 Facultative Pathogens

For facultative pathogens, the vector-pathogen relationship will differ dramatically from that of symbi-
otic pathogens. Likewise, their epidemiology also should differ dramatically. We propose an alternative
model for spread of facultative pentatomid-borne pathogens:

dS

dt

SaEaI

dE

dt

SaE

EI

N

dI

dt

EI

N

aI

=− ++

=−−

=−

β

β

δ

δ

(13.2)

The facultative model 13.2 differs from the symbiotic model 13.1 most drastically in that vector-
infection status is not included. Instead, we have added an additional compartment for exposed hosts,
E. Traditionally, exposed compartments in epidemic models have been used to model latent periods in
which hosts have been inoculated but are not yet infectious (e.g., Zeilinger and Daugherty 2014). Here,
we propose that susceptible hosts become fed upon by pentatomids at a rate β, which is a prerequisite

100 A

50

0

100

50

0

0 0.5 1

B

Parameter value

Pe

rcent

age Infe

cted

FIGURE 13.3 Percent infected hosts, I, from an epidemic model of pentatomid-associated facultative pathogens (13.2) at
varying values of (A) transmission rate, δ, and (B) herbivory rate, β. Values are taken as equilibrial (i.e., long-term) values
from numerical simulations after 2,000 time steps. Preliminary simulations using 10,000 time steps verified these equilib-
rial results. Other parameters were held constant: a = 0.1, S + I = 100; β = 0.4 when varying δ and vice-versa. R code for
models and simulations are available at https://github.com/arzeilinger/pentatomid_vector_epidemic_model.