Parameters

Description

${\pi }_h,{\pi }_v$

Recruitment rate of humans and vector respectively

${\pi }_{mh}$

Recruitment rate of migrated population

${\beta }_{hv}$

Transmission rate from host to vector

${\beta }_{vh}$

Transmission rate from vector to host

$b$

Biting rate of vector

${\upsilon }_h$

Proportion of antibody produced by human in the response to the incidence of infection caused by the vector

${\upsilon }_v$

Proportion of antibody produced by vector in the response to the incidence of infection caused by the human

${\mu }_h,{\mu }_v$

Natural death rate of humans and vector respectively

${\mu }_1,{\mu }_2$

Transition rates between exposed humans and infectious humans

${\sigma }_h$

Progression rate of exposed humans to infectious class

${\sigma }_v$

Progression rate of exposed vector to infectious class

${\tau }_h$

Treatment rate of the infectious individuals

$\omega$

Per captia rate of loss of immunity in humans

${\gamma }_1$

Recovery rate due to treatment

${\gamma }_m$

Mean aquatic transition rate

${\delta }_h,{\delta }_v$

Disease―induced death rate of humans and vectors respectively

$C_a,C_m$

Control effect rate

${\theta }_c$

Extrinsic incubation rate of vectors