A Deterministic Model for Q Fever Transmission Dynamics within Dairy Cattle Herds: Using Sensitivity Analysis and Optimal Controls

Table 1

Model parameter descriptions and values.

Parameter	Description	Range	Baseline value	Reference
β	Environmental transmission rate (indirect)	0.0030–0.0943	0.0943 day^−1/cattle	[19]
	Birth/recruitment rate	0.0034–0.0036	0.0036 day^−1	Estimated
η	Proportion of bacteria shed through mucus/faeces filling the environment	0.0021–0.0400	0.0400 day^−1/cattle	[19, 20]
ρ	Transition rate from A to S	0.0774–0.1208	0.1000 day^−1	[19, 20]
α	Transition rate A to I	0.0001–0.0117	0.0029 day^−1	[19, 20]
θ	Loss of vaccine immunity	0.0027–2.0000	0.0027 day^−1	[20]
μ	Natural death rate of cattle	0.0001–0.0002	0.0002 day^−1	Estimated
ν	Vaccination rate	0.1000–0.9000 unitless	0.1000	Assumed
ε	Environmental hygiene	0.1000–0.9000 unitless	0.1000	Assumed
Δ	Natural decay of bacteria from the dust/soil	0.0067–0.0083	0.0083 day^−1	Estimated
c	Culling/mortality rate	0.0008–0.0286	0.0286 day^−1	[20]