Modeling Gender-Structured Wildlife Diseases with Harvesting: Chronic Wasting Disease as an Example

Table 1

Parameter definitions.

Variable	Definition
𝑆𝑓(𝑡)	Number of susceptible female deer at time 𝑡
𝑆𝑚(𝑡)	Number of susceptible male deer at time 𝑡
𝐸𝑓(𝑡)	Number of exposed female deer at time 𝑡
𝐸𝑚(𝑡)	Number of exposed male deer at time 𝑡
𝐼𝑓(𝑡)	Number of infected female deer at time 𝑡
𝐼𝑚(𝑡)	Number of infected male deer at time 𝑡
𝑏	Fecundity
𝛽	Transmission rate
ℎ𝑓	Harvesting rate of females
ℎ𝑓	Harvesting rate of males
𝛽^𝑓𝐴	Transmissibility to females from an asymptomatic deer
𝛽^𝑓𝐼	Transmissibility to females from infected deer
𝛽^𝑚𝐴	Transmissibility to males from asymptomatic deer
𝛽^𝑚𝐼	Transmissibility to males from infected deer
𝛽𝐴	Rate of transmission from asymptomatic deer
𝛽𝐼	Rate of transmission from infected deer
𝛾𝑚𝑓	Rate of contact between infected males and susceptible females
𝛾𝑓𝑚	Rate of contact between infected females and susceptible males
𝛾𝑚	Rate of contact between infected males and susceptible males
𝛾𝑓	Rate of contact between infected females and susceptible females
𝐿	Incubation period
𝐿𝐸	Lifespan for exposed deer
𝐿𝐴	Lifespan for asymptomatic deer
𝜎	Rate of progression from exposed class to infected class
𝜎𝐸	Rate of progression from exposed class to asymptomatic class
𝜎𝐴	Rate of progression from asymptomatic class to infected class
𝜇𝑓	Natural death rate for females
𝜇𝑚	Natural death rate for males
𝜇𝑑	Death rate due to disease
𝛼𝑓^−1	Density-dependent reduction rate for females
𝛼𝑚^−1	Density-dependent reduction rate for males
𝑘^−1	Average harem size
𝜂	The probability that the newborn of an asymptomatic mother is susceptible