Abstract:
Malaria is mainly a tropical disease and its transmission cycle is
heavily influenced by environment: The life-cycles of the Anopheles
mosquito vector and Plasmodium parasite are both strongly affected
by ambient temperature, while suitable aquatic habitat is necessary
for immature mosquito development. Therefore, how global warming
may affect malaria burden is an active question, and we develop
a new ordinary differential equations-based malaria transmission
model that explicitly considers the temperature-dependent Anopheles
gonotrophic and Plasmodium sporogonic cycles. Mosquito
dynamics are coupled to infection among a human population with
symptomatic and asymptomatic disease carriers, as well as temporary
immunity. We also explore the effect of incorporating diurnal
temperature variations upon transmission. Rigorous analysis of the
model show that the non-trivial disease-free equilibrium is locallyasymptotically
stable when the associated reproduction number is
less than unity (this equilibrium is globally-asymptotically for a special
case with no density-dependent larval and disease-induced host
mortality). Numerical simulations of the model, for the case where
the ambient temperature is held constant, suggest a nonlinear,
hyperbolic relationship between the reproduction number and clinical
malaria burden. Moreover, malaria burden peaks at 29.5 oC when
daily ambient temperature is held constant, but this peak decreases
with increasing daily temperature variation, to about 23–25 oC.
Malaria burden also varies nonlinearly with temperature, such that
small temperature changes influent disease mainly at marginal temperatures,
suggesting that in areas where malaria is highly endemic,
any response to global warming may be highly nonlinear and most
typically minimal, while in areas of more marginal malaria potential
(such as the East African highlands), increasing temperatures may
translate nearly linearly into increased disease potential. Finally, we observe that while explicitly modelling the stages of the Plasmodium
sporogonic cycle is essential, explicitly including the stages of
the Anopheles gonotrophic cycle is of minimal importance.
