Here b1 is the recruitment rate of human population, susceptible human can
be infected by two ways of transmission, β1 which represents the direct transmission
from infected human and β2 is the rate of transmission from infected
vector. μh is the natural mortality rate of human, γh is the recovery rate of
human. In this work, we assumed that disease may be fatal to some infectious
host, so δh represents the disease related death rate of infected individuals. b2
is the recruitment rate of vector population. μv is the natural mortality rate of
vector population. The infectious vector die due to disease at a rate of δv, β3
represents the disease carrying of susceptible vector per host per unit time. γv
is the death rate of vector. The complete flow chart which show the interaction
of both human and vector are represented in Figure 1. The total dynamics of
human population is given by