Table 1. Model parameters and their numerical values.
Parameter | Interpretation | Units | Default values | Reference/notes |
---|---|---|---|---|
b | Influx of (susceptible) hosts | hosts ⋅ day−1 | 45.7 | Results in an equlibrium host density of 106 without the pathogen |
ψ, ϕ | Transmission constants governing acquisition of pathogen from infectious vectors to susceptible hosts (ψ), as well as the acquisition of pathogen from infectious hosts to susceptible vectors (ϕ) in the absence of genetic vector manipulation | day −1 | 0.2 | Inferred from type reproductive numbera |
d | Host background per-capita mortality rate | day−1 | [51, 52] | |
a | Pathogen induced per-capita host mortality rate | day−1 | 0.008549 | Based on [67], which reports of a 5% host mortality rate from dengue |
g | Natural infectious host recovery rate | day−1 | [51] | |
r | Intrinsic per-capita vector growth rate | day−1 | 0.835 | Midpoint of range in [99] |
k | Density-dependent effects on recruitment | (vectors ⋅ day)−1 | 3.675×10−7 | Based on an assumption of approximately 2 vectors per host |
μ | Vector per-capita mortality rate | day−1 | [44] and [96] | |
β | Parameter governing average vector competence immediately following the onset of the release of transgenic mosquitoes | − | −10 | Calibrated so that at t = 0, G(t) = 0.99995 (i.e., very close to 1). |
α | Parameter governing the decline in vector competence | day−1 | Varied | − |
ρ | The number of transgenic males carrying a dominant lethal construct released | − | Varied | − |
ϵ | Fraction of new hosts vaccinated | − | Varied | − |
δ | Medication-induced recovery rate | day−1 | Varied | − |
Parameters, their interpretations, units, and default values used in the numerical analysis. Unless stated otherwise, the default values represent the midpoint of the ranges reported in the relevant sources.
a For dengue, the number of secondary host infections arising from a single host infection (the type reproductive number) in the literature has typically been reported to range from less than 1 to greater than 10 (e.g., [51] and [40]). We present results in the main text for a type reproductive number of approximately 4.56.