Analysis of a model of gambiense sleeping sickness in humans and cattle.
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.
a Centre Régional de Formation Doctorale en Mathématiques et Informatique (C.R.F.D.M.I), Faculté des Sciences , Université de Kinshasa , Kinshasa , R.D. Congo.
A M
AM
Ndondo
b Department of Mathematical Sciences , University of South Africa , Florida , South Africa.
J M W
JM
Munganga
c Department of Science, Mathematics and Technology Education , University of Pretoria , Pretoria , South Africa.
J N
JN
Mwambakana
d Department of Mathematics and Statistics , University of Victoria , Victoria , BC , Canada.
C M
CM
Saad-Roy
d Department of Mathematics and Statistics , University of Victoria , Victoria , BC , Canada.
P
P
van den Driessche
a Centre Régional de Formation Doctorale en Mathématiques et Informatique (C.R.F.D.M.I), Faculté des Sciences , Université de Kinshasa , Kinshasa , R.D. Congo.
R O
RO
Walo
D000818:Animals; D002417:Cattle; D002418:Cattle Diseases / Q000635:transmission*; D006801:Humans; D007303:Insect Vectors / Q000469:parasitology; D008954:Models, Biological; D014347:Trypanosoma brucei gambiense / Q000302:isolation & purification*; D014353:Trypanosomiasis, African / Q000635:transmission* / Q000662:veterinary; D014370:Tsetse Flies / Q000254:growth & development / Q000469:parasitology
34D23; 92D30; Trypanosoma brucei gambiense; elasticity; global stability; sleeping sickness; vector-borne disease