Malaria and Sickle Cell Anemia - Dynamic Modeling of Diseases and Pests - page 60

REPRODUCTION RATE Ro

DD

HBI

Tm

Dm

TEMP

MEAL VECTOR

TEMP

REPELLENTS

T

BITING RATE VECTOR

TMIN

DAILY SURVIVAL VECTOR

X

BITING RATE VECTOR

TR

Y

VERT TO VECTOR

DAILY SURVIVAL VECTOR

VECTOR TO VERT

UNINFECTED POP

INFECTED POP

T

M

VECTOR UNINFECTED

Ro

VECTOR INFECTED

DAILY SURVIVAL VECTOR

Fig. 4.2

where the transmission rate TR is defined as

BITING RATE VECTOR ∧ 2 TR =( ) ∗ VERT TO VECTOR

(4.2)

DAILY SURVIVAL VECTOR ∧ T ∗ VECTOR TO VERT ∗ ( )

where VERT TO VECTOR and VECTOR TO VERT are, respectively, the probabil-
ity of transmission of parasites from infected vertebrates to uninfected vectors, and
from vectors to vertebrates 5 . For the model, these probabilities are assumed to be
fixed. In reality, though, these probabilities depend on absolute and relative vector
and vertebrate population densities.
M is the proportion of vectors to human hosts:
M

=( VECTOR INFECTED + VECTOR UNINFECTED ) /

(4.3)

( INFECTED POP + UNINFECTED POP )

The mosquito daily biting rate, in turn, is
BITINGRATEVECTOR = HBI ∗ MEAL VECTOR / REPELLENTS (4.4)

5 Rogers, D.J. and S.E. Randolph. 2000. The global spread of malaria in a future, warmer world.
Science 289:1763-1766.