Modeling San Joaquin Kit Fox Populations

The population size in Bakersfield was initiated at 400 San Joaquin kit foxes, i.e. 200 females (Table 2). Seasonal birth rate was calculated as ln(3.8/2 * the probability of an adult female birthing pups)/45 day window in which pups could be born, where 3.8 is mean llitter size and it is divided by 2 to estimate number of female pups born. We calculated the daily average natural death rate as -ln(total annual mortality) and dividing by 365 days.
Epidemiological parameters were also estimated from our data, other available data for the species, and where necessary, the most closely related species for which data were available (Table 3). We assumed that once exposed, kit foxes entered and then exited the E state such that the mean incubation time is 1⁄σ. Values of α_β were informed by observations of dispersal distance described in the section “Kit fox movement”, i.e. 1/α_β ~ mean dispersal distance. The reciprocal of α_β (i.e. α_β^-1) gives the mean transmission distance, since the decay over distance is assumed exponential. Thus α_β of 0.6 corresponds to a mean transmission distance of 1.67 kilometers, the distance from the center to the edge of one of our patches. The disease projection β/α_β is a transmission measure that takes into account local transmission and the geographic impact beyond local transmission. Values of β were derived: once there was an estimate of α_β, we calculated the value of β that produced output models that fit the observed epidemic history. Of note, concurrent to this study and data collection, we had applied a long-acting acaricide (flumethrin) to 17 kit foxes, which may have acted as a temporary form of “immunity”, essentially putting these kit foxes into an R class in the SEIR model [45 (link)].