摘要：Human African Trypanosomiasis (HAT) and Nagana in cattle, commonly called sleeping sickness, is caused by trypanosome protozoa
transmitted by bites of infected tsetse flies. We present a deterministic model for the transmission of HAT caused by Trypanosoma brucei
gambiense between human hosts, cattle hosts and tsetse flies. The
model takes into account the growth of the tsetse fly, from its larval stage to the adult stage. Disease in the tsetse fly population is
modeled by three compartments, and both the human and cattle
populations are modeled by four compartments incorporating the
two stages of HAT. We provide a rigorous derivation of the basic
reproduction number R0. For R0 < 1, the disease free equilibrium
is globally asymptotically stable, thus HAT dies out; whereas (assuming no return to susceptibility) for R0 > 1, HAT persists. Elasticity
indices for R0 with respect to different parameters are calculated
with baseline parameter values appropriate for HAT in West Africa;
indicating parameters that are important for control strategies to
bring R0 below 1. Numerical simulations with R0 > 1 show values
for the infected populations at the endemic equilibrium, and indicate that with certain parameter values, HAT could not persist in the
human population in the absence of cattle.
